Selecting Measures of Center & Variability for Data

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  • 0:04 Measures of Central Tendency
  • 0:35 Mean, Median & Mode
  • 1:27 Measures of Variability
  • 2:15 How to Choose a Measure
  • 3:43 Lesson Summary
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Lesson Transcript
Instructor: Betsy Chesnutt

Betsy teaches college physics, biology, and engineering and has a Ph.D. in Biomedical Engineering

In this lesson, learn about measures of central tendency like mean, median and mode. Learn how to calculate these measures and how to choose which ones to use in any situation.

Measures of Central Tendency

Susan is a third grade teacher, and in her classroom, there's a small library of books that students can check out to read. Susan decides to track the number of books checked out by each student for a month, recording all the data she collects in a table like this:


data table on books read


Once Susan has compiled her data, how can she determine the typical number of books checked out by the children in her class and summarize and present this information? Well, Susan can use one of the common measures of central tendency that represent the central position of a set of data.

Mean, Median & Mode

There are three important measures of central tendency commonly used to summarize a set of data: mean, median, and mode. The mean is the average of all the values. To find the mean of the data shown in this table, you'd add up the total number of books read and divide it by the number of students.


mean calculation


The median is the number that falls in the exact center of all the measurements. To find the median, arrange all of the data points from smallest to largest to find the one that's right in the middle. If there's an even number of measurements, choose the number that falls right between the two middle values.


median calculation


The third measure of central tendency is the mode of the data set, or the number that occurs most frequently. For Susan's data, the mode would be 3, because 4 students read 3 books and this was the most common number of books read. Although there was only one mode in this case, it's possible to have more than one if there were two or more data points that occurred the same number of times.

Measures of Variability

In addition to reporting the mean, median, or mode of a data set, it's often helpful to know something about how spread out the data is as well. There are several ways to measure a quantity known as variability, or the amount of spread in a set of data.

One way to describe the variability in a data set is to calculate the range, or the difference between the highest and lowest values in a data set. In our example, range = 8 - 0 = 8 books.

Another common measure of variability is known as standard deviation, which measures how far each one of the measurements is from the mean. If the standard deviation is low, it means that most of the values fall near the mean, so the variability is low. If a lot of the values are far from the mean, then the variability - and, therefore, the standard deviation - will be high.


standard deviation table


How to Choose a Measure

Now that you know about the common ways to measure central tendency and variability, how do you determine which one is best to use?

If the data follows a normal distribution, this means that the data points are equally distributed on each side of the mean.


normal distribution


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