Measures of Central Tendency: Mean, Median, and Mode
Introduction: Connecting Your Learning

In real-world applications, you can use tables and graphs of various kinds to show information and to extract information from data that can lead to analyses and predictions. Graphs allow you to communicate a message from data.

Measures of central tendency are a key way to discuss and communicate with graphs. The term central tendency refers to the middle, or typical, value of a set of data, which is most commonly measured by using the three m's: mean, median, and mode. The mean, median, and mode are known as the measures of central tendency. In this lesson, you will explore these three concepts.

Focusing Your Learning

Key Terms

Presentation

The Mean, Median, and Mode

Mean, median, and mode are three basic ways to look at the value of a set of numbers. You will start by learning about the mean.

For instance, take a look at the following example. Use the formula to calculate the mean number of hours that Stephen worked each month based on the example below.

The calculations for the mean of a sample and the total population are done in the same way. However, the mean of a population is constant, while the mean of a sample varies from sample to sample.

In addition to calculating the mean for a given set of data values, you can apply your understanding of the mean to determine other information that may be asked for in everyday problems.

All values for the means you have calculated so far have been for ungrouped, or listed, data. A mean can also be determined for data that is grouped, or placed in intervals. Unlike listed data, the individual values for grouped data are not available, and you are not able to calculate their sum. To calculate the mean of grouped data, the first step is to determine the midpoint of each interval or class. These midpoints must then be multiplied by the frequencies of the corresponding classes. The sum of the products divided by the total number of values will be the value of the mean.

The following example will show how the mean value for grouped data can be calculated.

The mean is often used as a summary statistic. However, it is affected by extreme values (outliers): either an unusually high or low number. When you have extreme values at one end of a data set, the mean is not a very good summary statistic.

The Median

What is the Median?

This measure of central tendency is typically used when the mean value is affected by an unusually low number or an unusually high number in the data set (outliers). Outliers distort the mean value to the extent that the mean value no longer accurately depicts the set of data.

For example: If one of the houses in your neighborhood was broken down and maintained a low property value, then you would not want to include this property when determining the value of your own home. However, if you are purchasing a home in that neighborhood, you may want to include the outlier since it would drive down the price you would have to pay.

Try a few examples to follow the steps needed to calculate the median.

Another way to look at the example is to narrow the data down to find the middle number.

Here is another example of how to calculate the median of a set of numbers.

The Mode

What is the Mode?

If two or more values appear with the same frequency, each is a mode. The downside to using the mode as a measure of central tendency is that a set of data may have no mode, or it may have more than one mode. However, the same set of data will have only one mean and only one median.

The word modal is often used when referring to the mode of a data set.

If a data set has only one value that occurs most often, the set is called unimodal.

A data set that has two values that occur with the same greatest frequency is referred to as bimodal.

When a set of data has more than two values that occur with the same greatest frequency, the set is called multimodal.

When determining the mode of a data set, calculations are not required, but keen observation is a must. The mode is a measure of central tendency that is simple to locate, but it is not used much in practical applications.