8.5: Percentiles
- Compute percentiles.
- Solve application problems involving percentiles.
A college admissions officer is comparing two students. The first, Anna, finished 12th in her class of 235 people. The second, Brian, finished 10th in his class of 170 people. Which of these outcomes is better? Certainly 10 is less than 12, which favors Brian, but Anna’s class was much bigger. In fact, Anna beat out 223 of her classmates, which is of her classmates, while Brian bested 160 out of 170 people, or 94%. Comparing the proportions of the data values that are below a given number can help us evaluate differences between individuals in separate populations. These proportions are called percentiles . If of the values in a dataset are less than a number , then we say that is at the th percentile.
Finding Percentiles
There are some other terms that are related to "percentile" with meanings you may infer from their roots. Remember that the word percent means “per hundred.” This reflects that percentiles divide our data into 100 pieces. The word quartile has a root that means “four.” So, if a data value is at the first quantile of a dataset, that means that if you break the data into four parts (because of the quart- ), this data value comes after the first of those four parts. In other words, it’s greater than 25% of the data, placing it at the 25th percentile. Quintile has a root meaning “five,” so a data value at the third quintile is greater than three-fifths of the data in the set. That would put it at the 60th percentile. The general term for these is quantiles (the root quant – means “number”).
In Mean, Median, and Mode, we defined the median as a number that is greater than no more than half of the data in a dataset and is less than no more than half of the data in the dataset. With our new term, we can more easily define it: The median is the value at the 50th percentile (or second quartile).
Let’s look at some examples.
Consider the dataset 5, 8, 12, 1, 2, 16, 2, 15, 20, 22.
- At what percentile is the value 5?
- What value is at the 60th percentile?
- Answer
-
Before we can answer these two questions, we must put the data in increasing order: 1, 2, 2, 5, 8, 12, 15, 16, 20, 22.
- There are three values (1, 2, and 2) in the set that are less than 5, and there are ten values in the set. Thus, 5 is at the percentile.
- To find the value at the 60th percentile, we note that there are ten data values, and 60% of ten is six. Thus, the number we want is greater than exactly six of the data values. Thus, the 60th percentile is 15.
Consider the dataset 2, 5, 8, 16, 12, 1, 8, 6, 15, 4.
- What value is at the 80th percentile?
At what percentile is the value 12?
In each of the examples above, the computations were made easier by the fact that the we were looking for percentiles that “came out evenly” with respect to the number of values in our dataset. Things don’t always work out so cleanly. Further, different sources will define the term percentile in different ways. In fact, Google Sheets has three built-in functions for finding percentiles, none of which uses our definition. Some of the definitions you’ll see differ in the inequality that is used. Ours uses “less than or equal to,” while others use “less than” (these correspond roughly to Google Sheets’ ‘PERCENTILE.INC’ and ‘PERCENTILE.EXC’). Some of them use different methods for interpolating values. (This is what we did when we first computed medians without technology; if there were an even number of data values in our dataset, found the mean of the two values in the middle. This is an example of interpolation. Most computerized methods use this technique.) Other definitions don’t interpolate at all, but instead choose the closest actual data value to the theoretical value. Fortunately, for large datasets, the differences among the different techniques become very small.
So, with all these different possible definitions in play, what will we use? For small datasets, if you’re asked to compute something involving percentiles without technology , use the technique we used in the previous example. In all other cases, we’ll keep things simple by using the built-in ‘PERCENTILE’ and ‘PERCENTRANK’ functions in Google Sheets (which do the same thing as the ‘PERCENTILE.INC’ and ‘PERCENTRANK.INC’ functions; they’re “inclusive, interpolating” definitions).
Using RANK, PERCENTRANK, and PERCENTILE in Google Sheets
The data in “AvgSAT” contains the average SAT score for students attending every institution of higher learning in the US for which data is available.
- What score is at the 3rd quartile?
- What score is at the 40th percentile?
- At what percentile is Albion College in Michigan (average SAT: 1132)?
- At what percentile is Oregon State University (average SAT: 1205)?
- Answer
-
- The 3rd quartile is the 75th percentile, so we’ll use the PERCENTILE function. Click on an empty cell, and type “=PERCENTILE(“. Next, enter the data: click on the letter at the top of the column containing the average SAT scores. Then, tell the function which percentile we want; it needs to be entered as a decimal. So, type a comma (to separate the two pieces of information we’re giving this function), then type “0.75” and close the parentheses with “)”. The result should look like this (assuming the data are in column C): “=PERCENTILE(C:C, 0.75)”. When you hit the enter key, the formula will be replaced with the average SAT score at the 75th percentile: 1199.
- Using the PERCENTILE function, we find that an average SAT of 1100 is at the 40th percentile.
- Since we want to know the percentile for a particular score, we’ll use the PERCENTRANK function. Like the PERCENTILE function, we need to give PERCENTRANK two pieces of information: the data, and the value we care about. So, click on an empty cell, type “=PERCENTRANK(“, and then click on the letter at the top of the column containing the data. Next, type a comma and then the value we want to find the percentile for; in this case, we’ll type “, 1132”. Finally, close the parentheses with “)” and hit the enter key. The formula will be replaced with the information we want: an average SAT of 1132 is at the 54th percentile.
- Using the PERCENTRANK function, an average SAT of 1205 is at the 76.1th percentile.
Looking again at the “AvgSAT” dataset:
- What score is at the 15th percentile?
- What score is at the 90th percentile?
- At what percentile is the University of Missouri (Columbia campus), whose average SAT score is 1244?
- At what percentile is Rice University in Texas, whose average SAT score is 1513?
The dataset "InState" contains the in-state tuitions of every college and university in the country that reported that data to the Department of Education. Use that dataset to answer these questions.
- What tuition is at the second quintile?
- What tuition is at the 95th percentile?
- At what percentile is Walla Walla University in Washington (in-state tuition: $28,035)?
- At what percentile is the College of Saint Mary in Nebraska (in-state tuition: $20,350)?
- Answer
-
- The second quintile is the 40th percentile; using PERCENTILE in Google Sheets, we get $8,400.
- Using PERCENTILE again, we get $44,866.
- Using PERCENTRANK, we get the 81.6th percentile.
- Using PERCENTRANK, we get the 74.8th percentile.
Looking again at the "InState" dataset, answer these questions.
- What tuition is at the 10th percentile?
- What tuition is at the fourth quintile?
- At what percentile is the main campus of New Mexico State University (in-state tuition: $6,686)?
- At what percentile is Bowdoin College in Maine (in-state tuition: $53,922)?
Check Your Understanding
1. Given the data 10, 12, 14, 18, 21, 23, 24, 25, 29, and 30, compute the following without technology:
The value at the 30th percentile
The value at the first quintile
At what percentile 29 falls
At what percentile 24 falls
For the remainder of these problems, use the dataset "MLB2019," which gives the number of wins for each Major League Baseball team in the 2019 season. Use Google Sheets to compute your answers.
- How many wins is at the 30th percentile?
- How many wins is at the 90th percentile?
- How many wins is at the first quartile?
- At what percentile are the Chicago Cubs (CHC, 84 wins)?
- At what percentile are the Tampa Bay Rays (TBR, 96 wins)?
- At what percentile are the Toronto Blue Jays (TOR, 67 wins)?


12.2: The Yuan Dynasty
Painting under the Yuan Dynasty
The Yuan Dynasty (1271–1368) saw the consolidation of poetry, painting, and calligraphy into a unified canon of classical Chinese art.
Discuss the fusion of styles in painting during the Yuan Dynasty, as well as the influencial artists who returned to the “blue and green” landscape style
Key Points
- The Yuan Dynasty was a time of important developments in the areas of painting, calligraphy , poetry, and theater, with many great artists practicing more than one medium .
- With the Yuan Dynasty, many artists retreated from social life and returned to nature through landscape paintings.
- Wang Meng was a leading painter of the Yuan Dynasty, and one of his most famous works is the Forest Grotto.
- Zhao Mengfu was a Chinese scholar, painter, and calligrapher who rejected the refined, gentle brushwork of his era in favor of the cruder style of the 8th century; he is considered to have brought about a revolution that created the modern Chinese landscape painting.
- Among the Yuan Dynasty artists, there were also the vivid and detailed works by Qian Xuan, who was famous for reviving and reproducing a more Tang Dynasty style of painting.
- The later Yuan Dynasty is characterized by the work of the so-called “Four Great Masters,” including Huang Gongwang, whose cool and restrained landscapes were admired by contemporaries and by the Chinese literati painters of later centuries.
Key Terms
- Wang Meng : (c. 1308–1385) A Chinese painter of the Yuan Dynasty who famously refused to serve the Mongolian rulers of their country.
- Yuan Dynasty : The empire established by Kublai Khan, the leader of the Mongolian Borjigin clan, after the Mongols conquered the Jin and Southern Song Dynasty in China; lasting from 1271 to 1368.
- Zhao Mengfu : (1254–1322) A Chinese prince and descendant of the Song Dynasty’s imperial family, and a scholar, painter, and calligrapher during the Yuan Dynasty.
Overview: The Yuan Dynasty (1271–1368)
With the fall of the Song Dynasty in 1279 and the subsequent dislocation caused by the establishment of the Yuan Dynasty by the Mongol conquerors, many court and literary artists retreated from social life. This was a time of important developments in the areas of painting, calligraphy, poetry, and theater, with many great artists practicing more than one medium. A great deal of artwork of the Yuan Dynasty has survived in China, relative to works from the Tang Dynasty and Song Dynasties, which have often been better preserved in places such as the Shōsōin in Japan.
Painting, Calligraphy, Poetry, and Theatre
One of the important cultural developments during the Yuan era was the consolidation of poetry, painting, and calligraphy into a unified piece that tends to come to mind when people think of classical Chinese art. The Song Dynasty and the Yuan Dynasty are linked together through the development of landscape painting, as well as the classical joining of calligraphy and poetry. In Yuan poetry, qu was the main development, which was used among other poetic forms by most of the famous Yuan poets. The qu form of poetry consists of words written in one of a number of certain, set tone patterns, based upon the tunes of various songs.
Many of the poets were also involved in the major developments in the theater during this time. Zazu was a form of Chinese drama or opera that provided entertainment through a synthesis of recitations of prose and poetry, dance, singing, and mime, with a certain emphasis on comedy or happy endings. One of the key factors in the common zaju variety shows was the incorporation of poetry both classical and of the newer qu form.
Influential Artists
Wang Meng was a famous painter of the Yuan Dynasty, and one of his most famous works is the Forest Grotto . Zhao Mengfu was a Chinese scholar, painter, and calligrapher, whose rejection of the refined, gentle brushwork of his era in favor of the cruder style of the 8th century is considered to have brought about a revolution that created the modern Chinese landscape painting. There was also the vivid and detailed works of art by Qian Xuan (1235–1305), who had served the Song court and out of patriotism refused to serve the Mongols. Instead, Qian Xuan turned to painting and became famous for his return to nature through landscape painting and his renewal of the “blue and green” style of the Tang Dynasty.
The later Yuan Dynasty is characterized by the work of the so-called “Four Great Masters.” The most notable of these was Huang Gongwang (1269–1354), whose cool and restrained landscapes were admired by contemporaries and by the Chinese literati painters of later centuries. Another man of great influence was Ni Zan (1301–1374), who frequently arranged his compositions with a strong and distinct foreground and background, leaving the middle ground as an empty expanse. This scheme was frequently adopted by later Ming and Qing Dynasty painters.
- Curation and Revision. Provided by : Boundless.com. License : CC BY-SA: Attribution-ShareAlike
- Wang Meng.nForest Grotto in Juqu.n1378.n68,8x42,5 National Palace Museum Taipei. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/File:Wang_Meng._Forest_Grotto_in_Juqu._1378._68,8x42,5_National_Palace_Museum_Taipei.jpg. License : Public Domain: No Known Copyright
- DwellingInTheFuchun. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/File:DwellingInTheFuchun.jpg. License : Public Domain: No Known Copyright
- Chinese art. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Chinese_art%23Yuan_painting. License : CC BY-SA: Attribution-ShareAlike
- Yuan Dynasty. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Yuan_Dynasty%23Culture. License : CC BY-SA: Attribution-ShareAlike
- Yuan Dynasty. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Yuan_Dynasty%23Culture. License : CC BY-SA: Attribution-ShareAlike
- Zhao Mengfu. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Zhao%20Mengfu. License : CC BY-SA: Attribution-ShareAlike
- Yuan Dynasty. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Yuan%20Dynasty. License : CC BY-SA: Attribution-ShareAlike
- Wang Meng. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Wang%20Meng. License : CC BY-SA: Attribution-ShareAlike


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9: Surface Morphology and Structure
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9.1: Interferometry
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The processes which occur at the surfaces of crystals depend on many external and internal factors such as crystal structure and composition, conditions of a medium where the crystal surface exists and others. The appearance of a crystal surface is the result of complexity of interactions between the crystal surface and the environment.
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9.2: Atomic Force Microscopy (AFM)
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Atomic force microscopy (AFM) is a high-resolution form of scanning probe microscopy, also known as scanning force microscopy (SFM).
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9.3: SEM and its Applications for Polymer Science
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The scanning electron microscope (SEM) is a very useful imaging technique that utilized a beam of electrons to acquire high magnification images of specimens. Very similar to the transmission electron microscope (TEM), the SEM maps the reflected electrons and allows imaging of thick (~mm) samples, whereas the TEM requires extremely thin specimens for imaging; however, the SEM has lower magnifications.
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9.4: Catalyst Characterization Using Thermal Conductivity Detector
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Metal dispersion is a commong term within the catalyst industry. The term refers to the amount of metal that is active for a specific reaction. Let’s assume a catalyst material has a composition of 1 wt% palladium and 99% alumina (Al2O3) (Figure 9.4.1 ) Even though the catalyst material has 1 wt% of palladium, not all the palladium is active.
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9.5: Nanoparticle Deposition Studies Using a Quartz Crystal Microbalance
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1.4.0: Vocabulario
|
Letters |
Names of Letters in Spanish |
Examples |
||
|---|---|---|---|---|
|
a |
a |
a rm a dillo |
Á l a mo |
S a n A ntonio |
|
b |
be, be larga |
b ota |
b urro |
b ailar |
|
c |
ce |
c aballo |
c actus |
c asería |
|
d |
de |
D allas |
Río Gran d e |
d isparo |
|
e |
e |
e xtenso |
e xplorar |
E ldorado |
|
f |
efe |
f ábrica |
f lor |
f amilia |
|
g |
ge |
g eneroso |
g ente |
G eneral Santa Ana |
|
h |
hache |
h eno |
h uerto |
co h ete |
|
i |
i |
i guana |
i ndependenc i a |
I rene |
|
j |
jota |
j aripeo |
j inete |
j ornalero |
|
k |
ca (ka) |
bi k ini |
K arina |
k ilo |
|
l |
ele |
L ibé l u l a |
L aredo |
l ibreta |
|
m |
eme |
m argarita |
ca m pesino |
m aestro |
|
n |
ene |
N evada |
N atalia |
N avarro |
|
ñ |
eñe |
ni ñ o |
ñ andú |
espa ñ ol |
|
o |
o |
O desa |
petr ó le o |
r o de o |
|
p |
pe |
El P aso |
p escador |
p atriota |
|
q |
cu |
q ueso |
Ra q uel |
Q uemado |
|
r |
erre |
ba rr il |
bece rr o |
co rr al |
|
s |
ese |
S arita |
S alado |
S an Benito |
|
t |
te |
T ejas |
t aco |
t ornado |
|
u |
u |
U valde |
ú nico |
u niversidad |
|
v |
uve, ve, or ve corta |
v aca |
v aquero |
v enado |
|
w |
uve doble, doble ve, or ve doble |
W ildorado |
W eslaco |
ki w i |
|
x |
equis |
ane x ar |
x ilofón |
E x tremadura |
|
y |
i griega or ye |
y egua |
Y ucatán |
y acaré |
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z |
zeta |
z oológico |
z acate |
cora z ón |
More information on the pronunciation of Spanish letters
Most letters in Spanish have only one pronunciation, and thus, spelling can be said to be easier in Spanish than in English. However, there are some exceptions:
- When c appears before a , o , u and the consonants l and r , it sounds like /k/ (e.g., carismático , Costa Rica , cultura , clima , crema ). When c is followed by e or i , it sounds like /s/ (e.g., centro , emocional ) in Latin America, but like /th/ in some parts of the world, when c is followed by h , it is pronounced like the ch in cheese (e.g., China ).
- When g appears before a , o , u and the consonants l and r, it sounds like an English hard /g/ (e.g., arrogante , amigo , gusto , globo , gracias ). When g is followed by e or i , it sounds like the English /h/ (e.g., generoso , ágil ). However, if a u is between g and e or i , g is pronounced like a hard /g/ , and the u is NOT pronounced (e.g., guía , espagueti ). Sometimes, in the combinations gue and gui , the u is pronounced if it is marked with a diéresis (the two dots above the ü ). In these cases, the g in combination with the u is pronounced /w/ . Examples: bilingüe , lingüística .
- Double l ( ll ) is pronounced like English /y/ in yes (e.g., me llamo , amarillo , pollo , calle ) . In some parts of Argentina and Uruguay, this sound is pronounced like /sh/ .
- Q can only be found in the combinations que and qui . In these cases, the u is silent, and the q is pronounced /k/ (e.g., ¿ qué ?, quinto [ fifth ]). Q cannot be followed by a , o , or u (unless u is followed by e or i ).
- When r is at the beginning or in the middle of a word and appears as a double r ( rr ), it is pronounced like a rolling r (e.g., Río Grande, Rosa , guitarra ).


5.1: Location-Scale Families
General Theory
As usual, our starting point is a random experiment modeled by a probability space \( (\Omega, \mathscr F, \P) \), so that \( \Omega \) is the set of outcomes, \( \mathscr F \) the collection of events, and \( \P \) the probability measure on the sample space \( (\Omega, \mathscr F) \). In this section, we assume that we fixed random variable \( Z \) defined on the probability space, taking values in \( \R \).
Definition
For \(a \in \R\) and \(b \in (0, \infty) \), let \(X = a + b \, Z\). The two-parameter family of distributions associated with \(X\) is called the location-scale family associated with the given distribution of \(Z\). Specifically, \(a\) is the location parameter and \(b\) the scale parameter .
Thus a linear transformation , with positive slope, of the underlying random variable \(Z\) creates a location-scale family for the underlying distribution. In the special case that \(b = 1\), the one-parameter family is called the location family associated with the given distribution, and in the special case that \(a = 0\), the one-parameter family is called the scale family associated with the given distribution. Scale transformations, as the name suggests, occur naturally when physical units are changed. For example, if a random variable represents the length of an object, then a change of units from meters to inches corresponds to a scale transformation. Location transformations often occur when the zero reference point is changed, in measuring distance or time, for example. Location-scale transformations can also occur with a change of physical units. For example, if a random variable represents the temperature of an object, then a change of units from Fahrenheit to Celsius corresponds to a location-scale transformation.
Distribution Functions
Our goal is to relate various functions that determine the distribution of \( X = a + b Z \) to the corresponding functions for \( Z \). First we consider the (cumulative) distribution function.
If \(Z\) has distribution function \(G\) then \(X\) has distribution function \(F\) given by \[ F(x) = G \left( \frac{x - a}{b} \right), \quad x \in \R\]
Proof
For \( x \in \R \) \[ F(x) = \P(X \le x) = \P(a + b Z \le x) = \P\left(Z \le \frac{x - a}{b}\right) = G\left(\frac{x - a}{b}\right) \]
Next we consider the probability density function. The results are a bit different for discrete distributions and continuous distribution, not surprising since the density function has different meanings in these two cases.
If \( Z \) has a discrete distribution with probability density function \( g \) then \( X \) also has a discrete distribution, with probability density function \( f \) given by \[ f(x) = g\left(\frac{x - a}{b}\right), \quad x \in \R \]
Proof
\( Z \) takes values in a countable subset \( S \subset \R \) and hence \( X \) takes values in \( T = \{a + b z: z \in S\} \), which is also countable. Moreover \[ f(x) = \P(X = x) = \P\left(Z = \frac{x - a}{b}\right) = g\left(\frac{x - a}{b}\right), \quad x \in \R \]
If \(Z\) has a continuous distribution with probability density function \(g\), then \(X\) also has a continuous distribution, with probability density function \(f\) given by
\[ f(x) = \frac{1}{b} \, g \left( \frac{x - a}{b} \right), \quad x \in \R\]- For the location family associated with \(g\), the graph of \(f\) is obtained by shifting the graph of \(g\), \(a\) units to the right if \(a \gt 0\) and \(-a\) units to the left if \(a \lt 0\).
- For the scale family associated with \(g\), if \(b \gt 1\), the graph of \(f\) is obtained from the graph of \(g\) by stretching horizontally and compressing vertically, by a factor of \(b\). If \(0 \lt b \lt 1\), the graph of \(f\) is obtained from the graph of \(g\) by compressing horizontally and stretching vertically, by a factor of \(b\).
Proof
First note that \( \P(X = x) = \P\left(Z = \frac{x - a}{b}\right) = 0 \), so \( X \) has a continuous distribution. Typically, \( Z \) takes values in an interval of \( \R \) and thus so does \( X \). The formula for the density function follows by taking derivatives of the distribution function above, since \( f = F^\prime \) and \( g = G^\prime \).
If \(Z\) has a mode at \(z\), then \(X\) has a mode at \(x = a + b z\).
Proof
This follows from density function in the discrete case or the density function in the continuous case. If \( g \) has a maximum at \( z \) then \( f \) has a maximum at \( x = a + b z \)
Next we relate the quantile functions of \(Z\) and \(X\).
If \(G\) and \(F\) are the distribution functions of \(Z\) and \(X\), respectively, then
- \(F^{-1}(p) = a + b \, G^{-1}(p)\) for \(p \in (0, 1)\)
- If \(z\) is a quantile of order \(p\) for \(Z\) then \(x = a + b \, z\) is a quantile of order \(p\) for \(X\).
Proof
These results follow from the distribution function above.
Suppose now that \( Z \) has a continuous distribution on \([0, \infty)\), and that we think of \(Z\) as the failure time of a device (or the time of death of an organism). Let \(X = b Z\) where \( b \in [0, \infty)\), so that the distribution of \(X\) is the scale family associated with the distribution of \(Z\). Then \(X\) also has a continuous distribution on \([0, \infty)\) and can also be thought of as the failure time of a device (perhaps in different units).
Let \(G^c\) and \(F^c\) denote the reliability functions of \(Z\) and \(X\) respectively, and let \(r\) and \(R\) denote the failure rate functions of \(Z\) and \(X\), respectively. Then
- \(F^c(x) = G^c(x / b)\) for \(x \in [0, \infty)\)
- \(R(x) = \frac{1}{b} r\left(\frac{x}{b}\right)\) for \(x \in [0, \infty)\)
Proof
Recall that \( G^c = 1 - G \), \( F^c = 1 - F \), \( r = g / \bar{G} \), and \( R = f / \bar{F} \). Thus the results follow from the distribution function and the density function above.
Moments
The following theorem relates the mean, variance, and standard deviation of \(Z\) and \(X\).
As before, suppose that \(X = a + b \, Z\). Then
- \(\E(X) = a + b \, \E(Z)\)
- \(\var(X) = b^2 \, \var(Z)\)
- \(\sd(X) = b \, \sd(Z)\)
Proof
These result follow immediately from basic properties of expected value and variance.
Recall that the standard score of a random variable is obtained by subtracting the mean and dividing by the standard deviation. The standard score is dimensionless (that is, has no physical units) and measures the distance from the mean to the random variable in standard deviations. Since location-scale familes essentially correspond to a change of units, it's not surprising that the standard score is unchanged by a location-scale transformation.
The standard scores of \(X\) and \(Z\) are the same:
\[ \frac{X - \E(X)}{\sd(X)} = \frac{Z - \E(Z)}{\sd(Z)} \]Proof
From the mean and variance above:
\[ \frac{X - \E(X)}{\sd(X)} = \frac{a + b Z - [a + b \E(Z)]}{b \sd(Z)} = \frac{Z - \E(Z)}{\sd(Z)} \]Recall that the skewness and kurtosis of a random variable are the third and fourth moments, respectively, of the standard score. Thus it follows from the previous result that skewness and kurtosis are unchanged by location-scale transformations: \(\skw(X) = \skw(Z)\), \(\kur(X) = \kur(Z)\).
We can represent the moments of \( X \) (about 0) to those of \( Z \) by means of the binomial theorem: \[ \E\left(X^n\right) = \sum_{k=0}^n \binom{n}{k} b^k a^{n - k} \E\left(Z^k\right), \quad n \in \N \] Of course, the moments of \( X \) about the location parameter \( a \) have a simple representation in terms of the moments of \( Z \) about 0: \[ \E\left[(X - a)^n\right] = b^n \E\left(Z^n\right), \quad n \in \N \] The following exercise relates the moment generating functions of \(Z\) and \(X\).
If \(Z\) has moment generating function \(m\) then \(X\) has moment generating function \(M\) given by
\[ M(t) = e^{a t} m(b t) \]Proof
\[ M(t) = \E\left(e^{tX}\right) = \E\left[e^{t(a + bZ)}\right] = e^{ta} \E\left(e^{t b Z}\right) = e^{a t} m(b t) \]Type
As we noted earlier, two probability distributions that are related by a location-scale transformation can be thought of as governing the same underlying random quantity, but in different physical units. This relationship is important enough to deserve a name.
Suppose that \( P \) and \( Q \) are probability distributions on \( \R \) with distribution functions \(F\) and \(G\), respectively. Then \( P \) and \( Q \) are of the same type if there exist constants \(a \in \R\) and \(b \in (0, \infty)\) such that \[ F(x) = G \left( \frac{x - a}{b} \right), \quad x \in \R \]
Being of the same type is an equivalence relation on the collection of probability distributions on \(\R\). That is, if \(P\), \(Q\), and \(R\) are probability distribution on \( \R \) then
- \(P\) is the same type as \(P\) (the reflexive property).
- If \(P\) is the same type as \(Q\) then \(Q\) is the same type as \(P\) (the symmetric property).
- If \(P\) is the same type as \(Q\), and \(Q\) is the same type as \(R\), then \(P\) is the same type as \(R\) (the transitive property).
Proof
Let \( F \), \( G \), and \( H \) denote the distribution functions of \( P \), \( Q \), and \( R \) respectively.
- This is trivial, of course, since we can take \( a = 0 \) and \( b = 1 \).
- Suppose there exists \( a \in \R \) and \( b \in (0, \infty) \) such that \( F(x) = G\left(\frac{x - a}{b}\right) \) for \( x \in \R \). Then \( G(x) = F(a + b x) = F\left(\frac{x - (-a/b)}{1/b}\right) \) for \( x \in \R \).
- Suppose there exists \( a, \, c \in \R \) and \( b, \, d \in (0, \infty) \) such that \( F(x) = G\left(\frac{x - a}{b}\right) \) and \( G(x) = H\left(\frac{x - c}{d}\right) \) for \( x \in \R \). Then \( F(x) = H\left(\frac{x - (a + bc)}{bd}\right)\) for \( x \in \R \).
So, the collection of probability distributions on \( \R \) is partitioned into mutually exclusive equivalence classes, where the distributions in each class are all of the same type.
Examples and Applications
Special Distributions
Many of the special parametric families of distributions studied in this chapter and elsewhere in this text are location and/or scale families.
The arcsine distribution is a location-scale family.
The Cauchy distribution is a location-scale family.
The exponential distribution is a scale family.
The exponential-logarithmic distribution is a scale family for each value of the shape parameter.
The extreme value distribution is a location-scale family.
The gamma distribution is a scale family for each value of the shape parameter.
The Gompertz distribution is a scale family for each value of the shape parameter.
The half-normal distribution is a scale family.
The hyperbolic secant distribution is a location-scale family.
The Lévy distribution is a location scale family.
The logistic distribution is a location-scale family.
The log-logistic distribution is a scale family for each value of the shape parameter.
The Maxwell distribution is a scale family.
The normal distribution is a location-scale family.
The Pareto distribution is a scale family for each value of the shape parameter.
The Rayleigh distribution is a scale family.
The semicircle distribution is a location-scale family.
The triangle distribution is a location-scale family for each value of the shape parameter.
The uniform distribution on an interval is a location-scale family.
The U-power distribution is a location-scale family for each value of the shape parameter.
The Weibull distribution is a scale family for each value of the shape parameter.
The Wald distribution is a scale family, although in the usual formulation, neither of the parameters is a scale parameter.


4.4: Conclusion and References
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- Gina Peterson and Emily Elam
- College of the Canyons
Monitoring, screening and evaluating children is both necessary and takes time and practice. Rather than waiting until there is a major concern, intentional teachers should conduct observations on a regular basis to closely monitor each child’s development. By watching children, we can find patterns. Once we understand the patterns, we can better understand why children do what they do, and ideally, we can create an inclusive learning environment that meets the needs of all our children. Understanding that over half of the children in your classroom may potentially have some special need, disability, delay or impairment is crucial. Recognizing that unless we observe regularly, we won’t be able to refer families in a timely manner to get the support services and professional help that they need is essential. Research tells us that children who receive early intervention are more likely to master age-appropriate developmental milestones, have i ncreased academic readiness and are more apt to socialize with their peers. It is important to remember that everyone in the classroom, including teachers, assistants and directors and supervisors, should be involved with monitoring a child’s development. As you continue to read this text, you will discover how observations are essential in planning effective curriculum, documenting children’s learning, assessing development and communicating with families. [49]
Referrals, Agencies and Support Groups [50]
Administration on Intellectual and Developmental Disabilities (AIDD)
AIDD seeks to improve and increase services for individuals with developmental disabilities that promote independence and inclusion in society. This website contains information on AIDD’s programs and other helpful resources, such as a developmental disabilities program directory by state and grants and funding information.
American Academy of Pediatrics
The American Academy of Pediatrics comprises pediatricians committed to the health of infants, children, adolescents, and young adults. The website contains general information about children’s health, as well as more specific information about guidelines, policies, and publications. This organization also hosts a website specifically for parents
Center for Parent Information and Resources (CPIR)
The CPIR serves as a central resource of information and products to the community of Parent Training Information Centers and the Community Parent Resource Centers, so that they can focus their efforts on serving families of children with disabilities.
Department of Education
The U.S. Department of Education (DOE) has resources to assist with the educational needs of children with developmental disabilities.
The DOE’s Technical Assistance and Dissemination Network (TA&D Network)
Provides links to a variety of other websites and online resources that focus on special education issues, such as policy, technology, curricula and parent trainings.
The DOE’s Office of Special Education and Rehabilitative Services (OSERS) Provides support to parents and individuals, school districts, and states in three main areas:
- Special education: Office of Special Education Programs (OSEP)external icon
- Vocational rehabilitation: Rehabilitation Services Administration (RSA)external icon
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DisabilityMeasures.org
DisabilityMeasures.org is an online resource with measurement tools for assessment, screening, and research concerning individuals with disabilities.
First Signs
First Signs is dedicated to educating parents and professionals about early identification and intervention for children at risk for developmental delays and disorders, including autism.
Insure Kids Now!
Each state provides no-cost or low-cost health insurance coverage for eligible children through Medicaid and the Children’s Health Insurance Program. This website has basic facts about these programs. It also has links to each state’s insurance program for children, where you can learn who is eligible for the programs, how to apply, and what services are covered. Information is available in English and Spanish.
MedlinePlus
MedlinePlus, a service of the U.S. National Library of Medicine and the National Institutes of Health, provides information on many different types of developmental disabilities, as well as resources on prevention and screening, research, statistics, law and policy, and more.
My Child Without Limits
My Child Without Limits provides resources for families of young children from birth through 5 years of age with developmental delays or disabilities, as well as for professionals who work with these individuals. The site also has a national resource locator where visitors can find local service providers, community organizations, and government agencies.
National Association of Councils on Developmental Disabilities (NACDD)
The NACDD supports state and territorial councils in implementing the Developmental Disabilities Assistance and Bill of Rights Act and promoting the interests and rights of individuals with disabilities and their families.
National Institute on Disability, Independent Living, and Rehabilitation Research (NIDILRR)external icon
NIDILRR is a federal government grants-making agency that sponsors grantees to generate new disability and rehabilitation knowledge and promote its use and adoption.
National Institutes of Health (NIH)
Several institutes within the NIH conduct and fund research about developmental disabilities. They also offer information to the public and educational programs for health professionals. They include:
National Eye Institute (NEI)
The NEI studies ways to prevent and treat eye diseases and vision problems and to improve the lives of people with these conditions.
National Institute of Child Health and Human Development (NICHD)
The NICHD conducts and supports research on all stages of human development to better understand the health of children, adults, families, and communities, including those with developmental disabilities.
National Institute on Deafness and Other Communication Disorders (NIDCD)
The NIDCD studies hearing loss, deafness, and problems with speech and language.
National Institute of Mental Health (NIMH)external icon
The NIMH studies mental illness and behavior problems, including such conditions as autism, attention-deficit/hyperactivity disorder, and learning disabilities.
National Institute of Neurological Disorders and Stroke (NINDS)external icon
NINDS studies the causes, diagnosis, treatment, and prevention of brain and nervous system disorders such as cerebral palsy and epilepsy.
References
- CDC. (n.d.) Developmental Monitoring. Retrieved from https://www.cdc.gov/ncbddd/childdevelopment/screening.html
- CDC. (n.d.). Developmental Monitoring and Screening. Retrieved from https://www.cdc.gov/ncbddd/actearly/pdf/Dev-Mon-and-Screen-English-and-Spanish-P.pdf


2.2: The Cell Membrane
By the end of the section, you will be able to:
- Describe the molecular components that make up the cell membrane
- Explain the major features and properties of the cell membrane
- Differentiate between materials that can and cannot diffuse through the lipid bilayer
- Compare and contrast different types of passive transport with active transport, providing examples of each
Despite differences in structure and function, all living cells in multicellular organisms have a surrounding cell membrane. As the outer layer of your skin separates your body from its environment, the cell membrane (also known as the plasma membrane) separates the inner contents of a cell from its exterior environment. This cell membrane provides a protective barrier around the cell and regulates which materials can pass in or out.
Structure and Composition of the Cell Membrane
The cell membrane is an extremely pliable structure composed primarily of back-to-back phospholipids (a “bilayer”). Cholesterol is also present, which contributes to the fluidity of the membrane, and there are various proteins embedded within the membrane that have a variety of functions.
A single phospholipid molecule has a phosphate group on one end, called the “head,” and two side-by-side chains of fatty acids that make up the lipid tails (Figure \(\PageIndex{1}\)). The phosphate group, which includes a phosphate and glycerol, is negatively charged, making the head polar and hydrophilic—or “water loving.” A hydrophilic molecule (or region of a molecule) is one that is attracted to water. The phosphate heads are thus attracted to the water molecules of both the extracellular and intracellular environments. The lipid tails, on the other hand, are uncharged, or nonpolar, and are hydrophobic—or “water fearing.” A hydrophobic molecule (or region of a molecule) repels and is repelled by water. Some lipid tails consist of saturated fatty acids, which form straight tails, and some contain unsaturated fatty acids, which form kinked tails. This combination adds to the fluidity of the tails that are constantly in motion. Phospholipids are thus amphipathic molecules. An amphipathic molecule is one that contains both a hydrophilic and a hydrophobic region. In fact, soap works to remove oil and grease stains because it has amphipathic properties. The hydrophilic portion can dissolve in water while the hydrophobic portion can trap grease in micelles that then can be washed away.
The cell membrane consists of two adjacent layers of phospholipids. The lipid tails of one layer face the lipid tails of the other layer, meeting at the interface of the two layers. The phospholipid heads face outward, one layer exposed to the interior of the cell and one layer exposed to the exterior ( Figure \(\PageIndex{2}\)). Because the phosphate groups are polar and hydrophilic, they are attracted to water in the intracellular fluid. Intracellular fluid (ICF) is the fluid interior of the cell. The phosphate groups are also attracted to the extracellular fluid. Extracellular fluid (ECF) is the fluid environment outside the enclosure of the cell membrane. Interstitial fluid (ISF) is the term given to extracellular fluid not contained within blood vessels. Because the lipid tails are hydrophobic, they meet in the inner region of the membrane, excluding watery intracellular and extracellular fluid from this space. The cell membrane has many proteins, as well as other lipids (such as cholesterol), that are associated with the phospholipid bilayer. An important feature of the membrane is that it remains fluid; the lipids and proteins in the cell membrane are not rigidly locked in place.
Membrane Proteins
The lipid bilayer forms the basis of the cell membrane, but it is peppered throughout with various proteins. Two different types of proteins that are commonly associated with the cell membrane are the integral proteins and peripheral proteins (Figure \(\PageIndex{3}\)). As its name suggests, an integral protein is a protein that is embedded in the membrane. A channel protein is an example of an integral protein that selectively allows particular materials, such as certain ions, to pass into or out of the cell.
Another important group of integral proteins are cell recognition proteins, which serve to mark a cell’s identity so that it can be recognized by other cells. A receptor is a type of recognition protein that can selectively bind a specific molecule outside the cell, and this binding induces a chemical reaction within the cell. A ligand is the specific molecule that binds to and activates a receptor. Some integral proteins serve dual roles as both a receptor and an ion channel. One example of a receptor-ligand interaction is the receptors on nerve cells that bind neurotransmitters, such as dopamine. When a dopamine molecule binds to a dopamine receptor protein, a channel within the transmembrane protein opens to allow certain ions to flow into the cell.
Some integral membrane proteins are glycoproteins. A glycoprotein is a protein that has carbohydrate molecules attached, which extend into the extracellular matrix. The attached carbohydrate tags on glycoproteins aid in cell recognition. The carbohydrates that extend from membrane proteins and even from some membrane lipids collectively form the glycocalyx. The glycocalyx is a fuzzy-appearing coating around the cell formed from glycoproteins and other carbohydrates attached to the cell membrane. The glycocalyx can have various roles. For example, it may have molecules that allow the cell to bind to another cell, it may contain receptors for hormones, or it might have enzymes to break down nutrients. The glycocalyces found in your body are products of your genetic makeup. They give each of your trillions of cells the “identity” of belonging in your body. This identity is the primary way that your immune defense cells “know” not to attack your own body cells, but it also is the reason organs donated by another person might be rejected.
Peripheral proteins are typically found on the inner or outer surface of the lipid bilayer but can also be attached to the internal or external surface of an integral protein. These proteins typically perform a specific function for the cell. Some peripheral proteins on the surface of intestinal cells, for example, act as digestive enzymes to break down nutrients to sizes that can pass through the cells and into the bloodstream.
Extensions of the Plasma Membrane
The plasma membrane is not always just a smooth round surface. Some cells may have extensions or folds of the plasma membrane, such as microvilli, flagella, or cilia. Microvilli are small folds in the plasma membrane that help to increase the surface area for purpose of transport of materials. Extensions like flagellum and cilia can be used to produce movement by the cytoskeleton, which is discussed further in another section of this chapter. You can compare the structure of these three extensions in Figure \(\PageIndex{4}\) below.
Transport across the Cell Membrane
One of the great wonders of the cell membrane is its ability to regulate the concentration of substances inside the cell. These substances include ions such as Ca ++ , Na + , K + , and Cl – ; nutrients including sugars, fatty acids, and amino acids; and waste products, particularly carbon dioxide (CO 2 ), that must leave the cell.
The membrane’s lipid bilayer structure provides the first level of control. The phospholipids are tightly packed together, and the membrane has a hydrophobic interior. This structure causes the membrane to be selectively permeable. A membrane that has selective permeability allows only substances meeting certain criteria to pass through it unaided. In the case of the cell membrane, only relatively small, nonpolar materials can move through the lipid bilayer (remember, the lipid tails of the membrane are nonpolar). Some examples of these are other lipids, oxygen and carbon dioxide gases, and alcohol. However, water-soluble materials—like glucose, amino acids, and electrolytes—need some assistance to cross the membrane because they are repelled by the hydrophobic tails of the phospholipid bilayer. All substances that move through the membrane do so by one of two general methods, which are categorized based on whether or not energy is required. Passive transport is the movement of substances across the membrane without the expenditure of cellular energy. In contrast, active transport is the movement of substances across the membrane using energy from adenosine triphosphate (ATP).
Passive Transport
In order to understand how substances move passively across a cell membrane, it is necessary to understand concentration gradients and diffusion. A concentration gradient is the difference in concentration of a substance across a space. Molecules (or ions) will spread/diffuse from where they are more concentrated to where they are less concentrated until they are equally distributed in that space. (When molecules move in this way, they are said to move down their concentration gradient.) Diffusion is the movement of particles from an area of higher concentration to an area of lower concentration. A couple of common examples will help to illustrate this concept. Imagine being inside a closed bathroom. If a bottle of perfume were sprayed, the scent molecules would naturally diffuse from the spot where they left the bottle to all corners of the bathroom, and this diffusion would go on until no more concentration gradient remains. Another example is a spoonful of sugar placed in a cup of tea. Eventually the sugar will diffuse throughout the tea until no concentration gradient remains. In both cases, if the room is warmer or the tea hotter, diffusion occurs even faster as the molecules are bumping into each other and spreading out faster than at cooler temperatures. Having an internal body temperature around 98.6 ° F thus also aids in diffusion of particles within the body.
Whenever a substance exists in greater concentration on one side of a semipermeable membrane, such as the cell membrane, any substance that can move down its concentration gradient across the membrane will do so. Consider substances that can easily diffuse through the lipid bilayer of the cell membrane, such as the gases oxygen (O 2 ) and CO 2 . O 2 generally diffuses into cells because it is more concentrated outside of them, and CO 2 typically diffuses out of cells because it is more concentrated inside of them. Neither of these examples requires any energy on the part of the cell, and therefore they use passive transport to move across the membrane.
Interactive Link
Diffusion
View this GIF showing the process of diffusion and how it is propelled by the kinetic energy of molecules in solution. How does temperature affect diffusion rate, and why?
- Answer
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Answer: Higher temperatures speed up diffusion because molecules have more kinetic energy at higher temperatures.
Before moving on, you need to review the gases that can diffuse across a cell membrane. Because cells rapidly use up oxygen during metabolism, there is typically a lower concentration of O 2 inside the cell than outside. As a result, oxygen, a small, non-polar substance, will diffuse from the interstitial fluid directly through the lipid bilayer of the membrane and into the cytoplasm within the cell. On the other hand, because cells produce CO 2 as a byproduct of metabolism, CO 2 concentrations rise within the cytoplasm; therefore, CO 2 will move from the cell through the lipid bilayer and into the interstitial fluid, where its concentration is lower. This mechanism of molecules spreading from where they are more concentrated to where they are less concentration is a form of passive transport called simple diffusion (Figure \(\PageIndex{5}\)).
Solutes dissolved in water on either side of the cell membrane will tend to diffuse down their concentration gradients, but because most substances cannot pass freely through the lipid bilayer of the cell membrane, their movement is restricted to protein channels and specialized transport mechanisms in the membrane. Facilitated diffusion is the diffusion process used for those substances that cannot cross the lipid bilayer due to their size and/or polarity (Figure \(\PageIndex{6}\)). A common example of facilitated diffusion is the movement of glucose into the cell, where it is used to make ATP. Although glucose can be more concentrated outside of a cell, it cannot cross the lipid bilayer via simple diffusion because it is both large and polar. To resolve this, a specialized carrier protein called the glucose transporter will transfer glucose molecules into the cell to facilitate its inward diffusion.
Facilitated diffusion is critical to the movement of charged ions such as sodium (Na + ). Even though sodium (Na + ) ions are small and highly concentrated outside of cells, these electrolytes are polarized and cannot pass through the nonpolar lipid bilayer of the membrane. Their diffusion is facilitated by membrane proteins that form sodium channels (or “pores”), so that Na + ions can move down their concentration gradient from outside the cells to inside the cells. There are many other solutes that must undergo facilitated diffusion to move into a cell, such as amino acids, or to move out of a cell, such as wastes. Because facilitated diffusion is a passive process, it does not require energy expenditure by the cell.
Water also can move freely across the cell membrane of all cells, either through protein channels or by slipping between the lipid tails of the membrane itself. Osmosis is the diffusion of water through a semipermeable membrane (Figure \(\PageIndex{7}\)).
The movement of water molecules is not itself regulated by cells, so it is important that cells are exposed to an environment in which the concentration of solutes outside of the cells (in the extracellular fluid) is equal to the concentration of solutes inside the cells (in the cytoplasm). Two solutions that have the same concentration of solutes are said to be isotonic (equal tension). When cells and their extracellular environments are isotonic, the concentration of water molecules is the same outside and inside the cells, and the cells maintain their normal shape (and function).
Osmosis occurs when there is an imbalance of solutes outside of a cell versus inside the cell. A solution that has a higher concentration of solutes than another solution is said to be hypertonic , and water molecules tend to diffuse into a hypertonic solution (Figure \(\PageIndex{8}\)). Cells in a hypertonic solution will shrivel as water leaves the cell via osmosis. In contrast, a solution that has a lower concentration of solutes than another solution is said to be hypotonic , and water molecules tend to diffuse out of a hypotonic solution. Cells in a hypotonic solution will take on too much water and swell, with the risk of eventually bursting. A critical aspect of homeostasis in living things is to create an internal environment in which all of the body’s cells are in an isotonic solution. Various organ systems, particularly the kidneys, work to maintain this homeostasis.
Another mechanism besides diffusion to passively transport materials between compartments is filtration. Unlike diffusion of a substance from where it is more concentrated to less concentrated, filtration uses a hydrostatic pressure gradient that pushes the fluid—and the solutes within it—from a higher pressure area to a lower pressure area. Filtration is an extremely important process in the body. For example, the circulatory system uses filtration to move plasma and substances across the endothelial lining of capillaries and into surrounding tissues, supplying cells with nutrients. Likewise, filtration pressure in the kidneys provides the mechanism to remove wastes from the bloodstream.
Active Transport
For all of the transport methods described above as passive transport, the cell expends no energy. Membrane proteins that aid in the passive transport of substances do so without the use of ATP. During active transport however, ATP is required to move a substance across a membrane. Whenever ATP is expended to actively move substances in or out of a cell, one or more membrane proteins will be involved in the transport process.
One of the most common types of active transport involves proteins that serve as pumps. The word “pump” probably conjures up thoughts of using energy to pump up the tire of a bicycle or a basketball, when energy is used to move air against a pressure gradient and inflate the tire or ball. Similarly, energy from ATP is required for these membrane proteins to transport substances—molecules or ions—across the membrane, usually against their concentration gradients (from an area of low concentration to an area of high concentration).
The sodium-potassium pump , which is also called Na + /K + ATPase, transports sodium out of a cell while moving potassium into the cell. The Na + /K + pump is an important ion pump found in the membranes of many types of cells. These pumps are particularly abundant in nerve cells, which are constantly pumping out sodium ions and pulling in potassium ions to maintain an electrical gradient across their cell membranes. An electrical gradient is a difference in electrical charge across a space. In the case of nerve cells, for example, the electrical gradient exists between the inside and outside of the cell, with the inside being negatively-charged (at around -70 mV) relative to the outside. The negative electrical gradient is maintained because each Na + /K + pump moves three Na + ions out of the cell and two K + ions into the cell for each ATP molecule that is used (Figure \(\PageIndex{9}\)). This process is so important for nerve cells that it accounts for the majority of their ATP usage.
Active transport pumps can also work together with other active or passive transport systems to move substances across the membrane. For example, the sodium-potassium pump maintains a high concentration of sodium ions outside of the cell. Therefore, if the cell needs sodium ions, all it has to do is open a passive sodium channel, as the concentration gradient of the sodium ions will drive them to diffuse into the cell. In this way, the action of an active transport pump (the sodium-potassium pump) powers the passive transport of sodium ions by creating a concentration gradient. When active transport powers the transport of another substance in this way, it is called secondary active transport.
Symporters are secondary active transporters that move two substances in the same direction. For example, the sodium-glucose symporter uses sodium ions to “pull” glucose molecules into the cell. Because cells store glucose for energy, glucose is typically at a higher concentration inside of the cell than outside. However, due to the action of the sodium-potassium pump, sodium ions will easily diffuse into the cell when the symporter is opened. The flood of sodium ions through the symporter provides the energy that allows glucose to move through the symporter and into the cell, against its concentration gradient.
Conversely, antiporters are secondary active transport systems that transport substances in opposite directions. For example, the sodium-hydrogen ion antiporter uses the energy from the inward flood of sodium ions to move hydrogen ions (H + ) out of the cell. The sodium-hydrogen antiporter is used to maintain the pH of the cell's interior.
Other forms of active transport do not involve membrane carriers. Endocytosis (bringing “into the cell”) is the process of a cell ingesting material by enveloping it in a portion of its cell membrane, and then pinching off that portion of membrane (Figure \(\PageIndex{10}\)). Once pinched off, the portion of membrane and its contents becomes an independent, intracellular vesicle. A vesicle is a membranous sac—a spherical and hollow organelle bounded by a lipid bilayer membrane. Endocytosis often brings materials into the cell that must to be broken down or digested. Phagocytosis (“cell eating”) is the endocytosis of large particles. Many immune cells engage in phagocytosis of invading pathogens. Like little Pac-men, their job is to patrol body tissues for unwanted matter, such as invading bacterial cells, phagocytize them, and digest them. In contrast to phagocytosis, pinocytosis (“cell drinking”) brings fluid containing dissolved substances into a cell through membrane vesicles.
Phagocytosis and pinocytosis take in large portions of extracellular material, and they are typically not highly selective in the substances they bring in. Cells regulate the endocytosis of specific substances via receptor-mediated endocytosis. Receptor-mediated endocytosis is endocytosis by a portion of the cell membrane that contains many receptors that are specific for a certain substance. Once the surface receptors have bound sufficient amounts of the specific substance (the receptor’s ligand), the cell will endocytose the part of the cell membrane containing the receptor-ligand complexes. Iron, a required component of hemoglobin, is endocytosed by red blood cells in this way. Iron is bound to a protein called transferrin in the blood. Specific transferrin receptors on red blood cell surfaces bind the iron-transferrin molecules, and the cell endocytoses the receptor-ligand complexes.
In contrast with endocytosis, exocytosis (taking “out of the cell”) is the process of a cell exporting material using vesicular transport (Figure \(\PageIndex{11}\)). Many cells manufacture substances that must be secreted, like a factory manufacturing a product for export. These substances are typically packaged into membrane-bound vesicles within the cell. When the vesicle membrane fuses with the cell membrane, the vesicle releases its contents into the interstitial fluid. The vesicle membrane then becomes part of the cell membrane. Cells of the stomach and pancreas produce and secrete digestive enzymes through exocytosis (Figure \(\PageIndex{12}\)). Endocrine cells produce and secrete hormones that are sent throughout the body, and certain immune cells produce and secrete large amounts of histamine, a chemical important for immune responses.
DISEASES OF THE CELL: Cystic Fibrosis
Cystic fibrosis (CF) affects approximately 30,000 people in the United States, with about 1,000 new cases reported each year. The genetic disease is most well known for its damage to the lungs, causing breathing difficulties and chronic lung infections, but it also affects the liver, pancreas, and intestines. Only about 50 years ago, the prognosis for children born with CF was very grim—a life expectancy rarely over 10 years. Today, with advances in medical treatment, average life expectancy for CF patients is in the late 30s and many live much longer.
The symptoms of CF result from a malfunctioning membrane ion channel called the cystic fibrosis transmembrane conductance regulator, or CFTR. In healthy people, the CFTR protein is an integral membrane protein that transports chloride (Cl – ) ions out of the cell. In a person who has CF, the gene for the CFTR is mutated, thus, the cell manufactures a defective channel protein that typically is not incorporated into the membrane, but is instead degraded by the cell.
The CFTR requires ATP in order to function, making its Cl – transport a form of active transport. This characteristic puzzled researchers for a long time because the Cl – ions are actually flowing down their concentration gradient when transported out of cells. Active transport generally pumps ions against their concentration gradient, but the CFTR presents an exception to this rule.
In normal lung tissue, the movement of Cl – out of the cell maintains a Cl – -rich, negatively charged environment immediately outside of the cell. This is particularly important in the epithelial lining of the respiratory system. Respiratory epithelial cells secrete mucus, which serves to trap dust, bacteria, and other debris. A cilium (plural = cilia) is one of the hair-like appendages found on certain cells. Cilia on the epithelial cells move the mucus and its trapped particles up the airways away from the lungs and toward the outside. In order to be effectively moved upward, the mucus cannot be too viscous; rather it must have a thin, watery consistency. The transport of Cl – and the maintenance of an electronegative environment outside of the cell attract positive ions such as Na + to the extracellular space. The accumulation of both Cl – and Na + ions in the extracellular space creates solute-rich mucus, which has a low concentration of water molecules. As a result, through osmosis, water moves from cells and extracellular matrix into the mucus, “thinning” it out. This is how, in a normal respiratory system, the mucus is kept sufficiently watered-down to be propelled out of the respiratory system.
If the CFTR channel is absent, Cl – ions are not transported out of the cell in adequate numbers, thus preventing them from drawing positive ions. The absence of ions in the secreted mucus results in the lack of a normal water concentration gradient. Thus, there is no osmotic pressure pulling water into the mucus. The resulting mucus is thick and sticky, and the ciliated epithelia cannot effectively remove it from the respiratory system. Passageways in the lungs become blocked with mucus, along with the debris it carries. Bacterial infections occur more easily because bacterial cells are not effectively carried away from the lungs.
Concept Review
The cell membrane provides a barrier around the cell, separating its internal components from the extracellular environment. It is composed of a phospholipid bilayer, with hydrophobic internal lipid “tails” and hydrophilic external phosphate “heads.” Various membrane proteins are scattered throughout the bilayer, both inserted within it and attached to it peripherally. The cell membrane is selectively permeable, allowing only a limited number of materials to diffuse through its lipid bilayer. All materials that cross the membrane do so using passive (non energy-requiring) or active (energy-requiring) transport processes. During passive transport, materials move by simple diffusion or by facilitated diffusion through the membrane, down their concentration gradient. Water passes through the membrane in a diffusion process called osmosis. During active transport, energy is expended to assist material movement across the membrane. Active transport may take place with the help of protein pumps or through the use of vesicles.
Review Questions
Q. Because they are embedded within the membrane, ion channels are examples of ________.
A. receptor proteins
B. integral proteins
C. peripheral proteins
D. glycoproteins
- Answer
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Answer: B
Q. The diffusion of substances within a solution tends to move those substances ________ their ________ gradient.
A. up; concentration
B. up; electrochemical
C. down; pressure
D. down; concentration
- Answer
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Answer: D
Q. Ion pumps and phagocytosis are both examples of ________.
A. endocytosis
B. passive transport
C. active transport
D. facilitated diffusion
- Answer
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Answer: C
Q. Choose the answer that best completes the following analogy: Diffusion is to ________ as endocytosis is to ________.
A. filtration; phagocytosis
B. osmosis; pinocytosis
C. solutes; fluid
D. gradient; chemical energy
- Answer
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Answer: B
Critical Thinking Questions
Q. What materials can easily diffuse through the lipid bilayer, and why?
- Answer
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A. Only materials that are relatively small and nonpolar can easily diffuse through the lipid bilayer. Large particles cannot fit in between the individual phospholipids that are packed together, and polar molecules are repelled by the hydrophobic/nonpolar lipids that line the inside of the bilayer.
Q. Why is receptor-mediated endocytosis said to be more selective than phagocytosis or pinocytosis?
- Answer
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A. Receptor-mediated endocytosis is more selective because the substances that are brought into the cell are the specific ligands that could bind to the receptors being endocytosed. Phagocytosis or pinocytosis, on the other hand, have no such receptor-ligand specificity, and bring in whatever materials happen to be close to the membrane when it is enveloped.
Q. What do osmosis, diffusion, filtration, and the movement of ions away from like charge all have in common? In what way do they differ?
- Answer
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A. These four phenomena are similar in the sense that they describe the movement of substances down a particular type of gradient. Osmosis and diffusion involve the movement of water and other substances down their concentration gradients, respectively. Filtration describes the movement of particles down a pressure gradient, and the movement of ions away from like charge describes their movement down their electrical gradient.
Glossary
- active transport
- form of transport across the cell membrane that requires input of cellular energy
- amphipathic
- describes a molecule that exhibits a difference in polarity between its two ends, resulting in a difference in water solubility
- cell membrane
- membrane surrounding all animal cells, composed of a lipid bilayer interspersed with various molecules; also known as plasma membrane
- channel protein
- membrane-spanning protein that has an inner pore which allows the passage of one or more substances
- cilia
- small appendage on certain cells formed by microtubules and modified for movement of materials across the cellular surface
- concentration gradient
- difference in the concentration of a substance between two regions
- diffusion
- movement of a substance from an area of higher concentration to one of lower concentration
- electrical gradient
- difference in the electrical charge (potential) between two regions
- endocytosis
- import of material into the cell by formation of a membrane-bound vesicle
- exocytosis
- export of a substance out of a cell by formation of a membrane-bound vesicle
- extracellular fluid (ECF)
- fluid exterior to cells; includes the interstitial fluid, blood plasma, and fluid found in other reservoirs in the body
- facilitated diffusion
- diffusion of a substance with the aid of a membrane protein
- flagellum
- appendage on certain cells formed by microtubules and modified for movement
- glycocalyx
- coating of sugar molecules that surrounds the cell membrane
- glycoprotein
- protein that has one or more carbohydrates attached
- hydrophilic
- describes a substance or structure attracted to water
- hydrophobic
- describes a substance or structure repelled by water
- hypertonic
- describes a solution concentration that is higher than a reference concentration
- hypotonic
- describes a solution concentration that is lower than a reference concentration
- integral protein
- membrane-associated protein that spans the entire width of the lipid bilayer
- interstitial fluid (IF)
- fluid in the small spaces between cells not contained within blood vessels
- intracellular fluid (ICF)
- fluid in the cytosol of cells
- isotonic
- describes a solution concentration that is the same as a reference concentration
- ligand
- molecule that binds with specificity to a specific receptor molecule
- microvilli
- small folds in the plasma membrane that help to increase surface area
- osmosis
- diffusion of molecules down their concentration across a selectively permeable membrane
- passive transport
- form of transport across the cell membrane that does not require input of cellular energy
- peripheral protein
- membrane-associated protein that does not span the width of the lipid bilayer, but is attached to the inside or outside of the membrane by way of integral proteins, membrane lipids, or other components of the membrane
- phagocytosis
- endocytosis of large particles
- pinocytosis
- endocytosis of fluid
- receptor
- protein molecule that contains a binding site for another specific molecule (called a ligand)
- receptor-mediated endocytosis
- endocytosis of ligands attached to membrane-bound receptors
- selective permeability
- feature of any barrier that allows certain substances to cross but excludes others
- sodium-potassium pump
- (also, Na + /K + ATP-ase) membrane-embedded protein pump that uses ATP to move Na + out of a cell and K + into the cell
- vesicle
- membrane-bound structure that contains materials within or outside of the cell
Contributors and Attributions
-
OpenStax Anatomy & Physiology (CC BY 4.0). Access for free at https://openstax.org/books/anatomy-and-physiology


1.1: The Foundations of Communication Overview
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You are probably reading this book because you are taking an introductory Communication course at your college or university. Many colleges and universities around the country require students to take some type of communication course in order to graduate. Introductory Communication classes include courses on public speaking, interpersonal communication, or a class that combines both. While these are some of the most common introductory Communication courses, many Communication departments are now offering an introductory course that explains what Communication is, how it is studied as an academic field, and what areas of specialization make up the field of Communication. In other words, these are survey courses similar to courses such as Introduction to Sociology or Introduction to Psychology. Our goal in this text is to introduce you to the field of Communication as an academic discipline of study.
Engaging in Conversation
As professors, we hear a lot of people talk about communication both on and off our campuses. We’re often surprised at how few people can actually explain what communication is, or what Communication departments are about. Even our majors sometimes have a hard time explaining to others what it is they study in college. Throughout this book we will provide you with the basics for understanding what communication is, what Communication scholars and students study, and how you can effectively use the study of Communication in your life — whether or not you are a Communication major. We accomplish this by taking you on a journey through time. The material in the text is framed chronologically, and is largely presented in context of the events that occurred before the industrial revolution (2500 BCE-1800’s), and after the industrial revolution (1800’s-Present). In each chapter we include boxes that provide examples on that chapter’s topic in context of “then,” “now,” and “you” to help you grasp how the study of Communication at colleges and universities impacts life in the “real world.”
To make it easier for you to have a general understanding of Communication study as an academic field, we divide the book into two parts: Chapters 1–6 provide you with the foundations of Communication as an academic field of study. In this chapter you will learn the definitions of Communication and Communication study, as well as understand possible careers that result from studying Communication. In Chapters 2 and 3 you will learn that verbal and nonverbal communication are the primary human acts we study in Communication. The history of Communication study in Chapter 4 lets you see the chronological development of the field, which determined our choices for how we ordered the chapters in Part II. Finally, Chapters 5 and 6 briefly highlight the different theories and research methods we use to study human communication.
Chapters 7–13 highlight many of the prominent Communication specializations that have shaped the field in the past 100 years. We present them in the chronological order in which they became part of the Communication discipline. While there are many more areas of specialization we would like to cover in this text, we have chosen to highlight the ones that have shaped what you likely recognize as part of the Communication departments at your colleges and universities. Because we cannot cover every specialization, we chose to include ones that were instrumental in the earlier development of the field that are still being explored today, as well as specializations we believe represent new directions in the field that examine communication in our ever-changing society.
Before we introduce you to verbal and nonverbal communication, history, theories, research methods, and the chronological development of Communication specializations, we want to set a foundation for you in this chapter by explaining Communication Study, Models of Communication, and Communication at work.
Contributions and Affiliations
- Survey of Communication Study. Authored by : Scott T Paynton and Linda K Hahn. Provided by : Humboldt State University. Located at : en.wikibooks.org/wiki/Survey_of_Communication_Study. License : CC BY-SA: Attribution-ShareAlike
- Image of women. Authored by : Peter van der Sluijs. Located at : commons.wikimedia.org/wiki/File:Women_in_Jerusalem.JPG. License : CC BY-SA: Attribution-ShareAlike


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2.3: Review- Counting Syllables and Identifying Stress
Counting Syllables and Identifying stress.
- Write the correct number of syllables for each word.
- Then divide each word into syllables.
- Underline the syllable with the most stress.
| Question Number | Word | Number of Syllables | Divide the word into syllables |
|---|---|---|---|
| EXAMPLE: | computer | 3 | com- pu -ter |
| 1 | sustainable | ||
| 2 | industrial | ||
| 3 | agriculture | ||
| 4 | values | ||
| 5 | harvest | ||
| 6 | repair | ||
| 7 | produce | ||
| 8 | podcasts | ||
| 9 | challenging | ||
| 10 | vegan | ||
| 11 | water | ||
| 12 | environmental | ||
| 13 | impact | ||
| 14 | production | ||
| 15 | pollutes | ||
| 16 | fences | ||
| 17 | carbon | ||
| 18 | habitats |


2.1: Introduction and Historical Context
| Event in History | Events in music |
|
From the 1st Century CE: Spread of Christianity through the Roman Empire 4th Century CE: Founding of the monastic movement in Christianity c. 450 CE: Fall of Rome 11th Century CE: Rise of Feudalism & the Three Estates 11th Century CE: Growth of Marian Culture 1088 CE: Founding of the University of Bologna c. 1095-1291 CE: The Crusades c. 1163-1240s CE: Building of Notre Dame in Paris and the rise of Gothic architecture 13th Century CE: Development of Polyphony 1346-53: Height of the Bubonic Plague (Black Death) |
2nd millennia BCE: First Hebrew Psalms are written 7th Century BCE: Ancient Greeks and Romans use music for entertainment and religious rites 6th Century BCE: Pythagoras and his experiments with acoustics 4th Century BCE: Plato and Aristotle write about music c. 400 CE: St Augustine writes about church music 4th – 9th Century CE: Development/Codification of Christian Chant c. 800 CE: First experiments in Western Music 11st Century CE: Guido of Arezzo refines of mu11 sic notation and development of solfège 12th Century CE: Hildegard of Bingen writes Gregorian chnat 13th Century CE: Development of Polyphony c. 1275 CE: King Alfonso the Wise collects early songs in an exquisitely illuminated manuscript 14th Century CE: Further refinement of musical notation, including notation for rhythm 1300-1377 CE: Guillaume de Machaut composes songs and church music |
Introduction
What do you think of when you hear the term the Middle Ages (450-1450)? For some, the semi-historical figures of Robin Hood and Maid Marian come to mind. Others recall Western Christianity’s Crusades to the Holy Land. Still others may have read about the arrival in European lands of the bubonic plague or Black Death, as it was called. For most twenty-first-century individuals, the Middle Ages seem far removed. Although life and music were quite different back then, we hope that you will find that there are cultural threads that extend from that distant time to now.
We normally start studies of Western music with the Middle Ages, but of course, music existed long before then. In fact, the term Middle Ages or medieval period got its name to describe the time in between (or “in the middle of”) the ancient age of classical Greece and Rome and the Renaissance of Western Europe, which roughly began in the fifteenth century. Knowledge of music before the Middle Ages is limited but what we do know largely revolves around the Greek mathematician Pythagoras, who died around 500 B.C.E. (See his profile on a third century ancient coin: Figure 2.1.1)
Pythagoras might be thought of as a father of the modern study of acoustics due to his experimentation with bars of iron and strings of different lengths. Images of people singing and playing instruments, such as those found on the Greek vases provide evidence that music was used for ancient theater, dance, and worship. The Greek word musicka referred to not music but also referred to poetry and the telling of history. Writings of Plato and Aristotle referred to music as a form of ethos (an appeal to ethics). As the Roman Empire expanded across Western Europe, so too did Christianity (see Figure 2.1.2, a map of Western Europe around 1000). Considering that Biblical texts from ancient Hebrews to those of early Christians, provided numerous records of music used as a form of worship, the Empire used music to help unify its people: the theory was that if people worshipped together in a similar way, then they might also stick together during political struggles.
Later, starting around 800 CE, Western music is recorded in a notation that we can still decipher today. This brief overview of these five hundred years of the Roman Empire will help us better understand the music of the Middle Ages.
Historical Context for Music of the Middle Ages (800-1400)
During the Middle Ages, as during other periods of Western history, sacred and secular worlds were both separate and integrated. However during this time, the Catholic Church was the most widespread and influential institution and leader in all things sacred. The Catholic Church’s head, the Pope, maintained political and spiritual power and influence among the noble classes and their geographic territories; the life of a high church official was not completely different from that of a noble counterpart, and many younger sons and daughters of the aristocracy found vocations in the church. Towns large and small had churches, spaces open to all: commoners, clergy, and nobles. The Catholic Church also developed a system of monasteries, where monks studied and prayed, often in solitude, even while making cultural and scientific discoveries that would eventually shape human life more broadly. In civic and secular life, kings, dukes, and lords wielded power over their lands and the commoners living therein. Kings and dukes had courts, gatherings of fellow nobles, where they forged political alliances, threw lavish parties, and celebrated both love and war in song and dance.
Many of the important historical developments of the Middle Ages arose from either in the church or the court. One such important development stemming from the Catholic Church would be the developments of architecture. During this period, architects built increasingly tall and imposing cathedrals for worship through the technological innovations of pointed arches, flying buttresses, and large cut glass windows. This new architectural style was referred to as “gothic,” which vastly contrast the Romanesque style, with its rounded arches and smaller windows. Another important development stemming from the courts occurred in the arts. Poets and musicians, attached to the courts, wrote poetry, literature, and music, less and less in Latin—still the common language of the church—and increasingly in their own vernacular languages (the predecessors of today’s French, Italian, Spanish, German, and English). However, one major development of the Middle Ages spanned sacred and secular worlds: universities shot up in locales from Bologna, Italy, and Paris, France, to Oxford, England (the University of Bologna begin the first). At university, a young man could pursue a degree in theology, law, or medicine. Music of a sort was studied as one of the seven liberal arts and sciences, specifically as the science of proportions. (Look for music in this twelfth-century image of the seven liberal arts from the Hortus deliciarum of the Herrad of Landsberg (Figure \(\PageIndex{5}\)).


1.6: Exercises
Let \(p\text{,}\) \(q\text{,}\) and \(r\) represent the following statements.
\begin{align*} p\colon\quad & \text{The game is on.} \\ q\colon\quad & \text{The popcorn is ready.} \\ r\colon\quad & \text{Joe is happy.} \end{align*}
Suppose the following compound statement is true.
If the game is on and the popcorn is ready, then Joe is happy.
However, you just visited Joe's residence room and found that Joe is unhappy even though the game is on. What can you conclude about the popcorn? Use a truth table to justify your answer.
Consider the logical statement \((p \land q_1) \rightarrow (q_1 \lor q_2)\text{.}\) Partially translated, this statement says:
if \(p\) and \(q_1\) are both true, then at least one of \(q_1\) and \(q_2\) is true.
Would you expect this statement to be a tautology? … a contradiction? … neither?
Use a truth table to check.
The wizard Hatty Porrer is studying logic at Cowpimples School for Second-Rate Wizards. As an exercise, he is filling out the truth table for the conditional
\begin{equation*} (r \land s) \rightarrow (r \lor s) \text{.} \end{equation*}
But he forgets what to do for the lines where the “if” part of the conditional evaluates to false, so he only gets this far:
| \(r\) | \(s\) | \(r \land s\) | \(r \lor s\) | \((r \land s) \rightarrow (r \lor s)\) |
| \(T\) | \(T\) | \(T\) | \(T\) | \(T\) |
| \(T\) | \(F\) | \(F\) | \(T\) | ? |
| \(F\) | \(T\) | \(F\) | \(T\) | ? |
| \(F\) | \(F\) | \(F\) | \(F\) | ? |
- Help Hatty out by finishing his homework for him.
- While you were filling out the truth table, Hatty got bored and opened up a portal to a parallel universe. Parallel Hatty is also working on the same truth table, and is stuck at the same spot that normal Hatty was. However, you notice that parallel Hatty's textbook is open to the page with the truth table for the basic conditional \(p \rightarrow q\text{,}\) and it looks as follows.
| \(p\) | \(q\) | \(p \rightarrow q\) |
| \(T\) | \(T\) | \(T\) |
| \(T\) | \(F\) | \(F\) |
| \(F\) | \(T\) | \(F\) |
| \(F\) | \(F\) | \(T\) |
Finish parallel Hatty's homework exercise. Make sure parallel Hatty's instructor will like the result!
- While you were finishing parallel Hatty's homework, Hatty got bored again and opened up a portal to another parallel universe! Parallel Hatty number two is also working on the same truth table, and is stuck at the same spot that the previous two Hattys were. This time, however, parallel Hatty number two's textbook says that the truth table for the basic conditional \(p \rightarrow q\) is as follows.
| \(p\) | \(q\) | \(p \rightarrow q\) |
| \(T\) | \(T\) | \(T\) |
| \(T\) | \(F\) | \(F\) |
| \(F\) | \(T\) | \(T\) |
| \(F\) | \(F\) | \(F\) |
Finish parallel Hatty number two's homework exercise. Make sure parallel Hatty number two's instructor will approve!
- You'll never believe what happened while you were finishing parallel Hatty number two's homework! Yep, Hatty got bored again and opened up a portal to a third parallel universe. Parallel Hatty number three is also working on the same truth table, and is stuck at the same spot that the previous three Hattys were. The truth table for the basic conditional \(p \rightarrow q\) is different in parallel Hatty number three's universe, yet again.
| \(p\) | \(q\) | \(p \rightarrow q\) |
| \(T\) | \(T\) | \(T\) |
| \(T\) | \(F\) | \(F\) |
| \(F\) | \(T\) | \(F\) |
| \(F\) | \(F\) | \(F\) |
Finish parallel Hatty number three's homework exercise. Make sure parallel Hatty number three's instructor will give him full marks!
- OK, so what the heck is the point of all this? The statement \((r \land s) \rightarrow (r \lor s)\) could be read as:
If \(r\) and \(s\) are both true statements, then at least one of \(r\) and \(s\) is a true statement.
This conditional statement seems “obviously true”. Based on this example, what do you think of each parallel universe's system of logic compared to our own?
Suppose \(A,E,U\) are logical statements such that \(U\) is a tautology and \(E\) is a contradiction.
- Show that \(A \lor U\) is always a tautology.
- Show that \(A \land E\) is always a contradiction.
Suppose that \(A\text{,}\) \(B\text{,}\) and \(C\) are logical statements such that \(A \Rightarrow B\) and \(B \Rightarrow C\text{.}\) Must \(A \Rightarrow C\text{?}\)