Central Tendency: Measures, Definition & Examples

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  • 0:01 What Is Central Tendency?
  • 0:58 Why Is It Important?
  • 2:23 Three Measures
  • 9:02 Mode
  • 10:29 Lesson Summary
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Lesson Transcript
Instructor: Yolanda Williams

Yolanda has taught college Psychology and Ethics, and has a doctorate of philosophy in counselor education and supervision.

Explore the measures of central tendency. Learn more about mean, median, and mode and how they are used in the field of psychology. At the end, test your knowledge with a short quiz.

What Is Central Tendency?

Think about how you describe a single piece of numerical data. This is usually done in terms of its value. For example, in order to describe the number 2, you might put up two fingers or you might say 2 = 1 + 1. How would you describe a group of data? It would not be beneficial to use your fingers in this instance. Nor is it beneficial to simply add the data together. However, you can describe a group of data in a single value by using measures of central tendency.

So, what exactly is a measure of central tendency? A measure of central tendency is a single value that describes the way in which a group of data cluster around a central value. To put in other words, it is a way to describe the center of a data set. There are three measures of central tendency: the mean, the median, and the mode.

Why Is Central Tendency Important?

Central tendency is very useful in psychology. It lets us know what is normal or 'average' for a set of data. It also condenses the data set down to one representative value, which is useful when you are working with large amounts of data. Could you imagine how difficult it would be to describe the central location of a 1000-item data set if you had to consider every number individually?

Central tendency also allows you to compare one data set to another. For example, let's say you have a sample of girls and a sample of boys, and you are interested in comparing their heights. By calculating the average height for each sample, you could easily draw comparisons between the girls and boys.

Central tendency is also useful when you want to compare one piece of data to the entire data set. Let's say you received a 60% on your last psychology quiz, which is usually in the D range. You go around and talk to your classmates and find out that the average score on the quiz was 43%. In this instance, your score was significantly higher than those of your classmates. Since your teacher grades on a curve, your 60% becomes an A. Had you not known about the measures of central tendency, you probably would have been really upset by your grade and assumed that you bombed the test.

Three Measures of Central Tendency

Let's talk more about the different measures of central tendency. You are probably already familiar with the mean, or average. The mean is calculated in two steps:

  1. Add the data together to find the sum
  2. Take the sum of the data and divide it by the total number of data

Now let's see how this is done using the height example from earlier. Let's say you have a sample of ten girls and nine boys.

The girls' heights in inches are: 60, 72, 61, 66, 63, 66, 59, 64, 71, 68.

Here are the steps to calculate the mean height for the girls:

First, you add the data together: 60 + 72 + 61 + 66 + 63 + 66 + 59 + 64 + 71 + 68 = 650. Then, you take the sum of the data (650) and divide it by the total number of data (10 girls): 650 / 10 = 65. The average height for the girls in the sample is 65 inches. If you look at the data, you can see that 65 is a good representation of the data set because 65 lands right around the middle of the data set.

The mean is the preferred measure of central tendency because it considers all of the values in the data set. However, the mean is not without limitations. In order to calculate the mean, data must be numerical. You cannot use the mean when you are working with nominal data, which is data on characteristics like gender, appearance, and race. For example, there is no way that you can calculate the mean of the girls' eye colors. The mean is also very sensitive to outliers, which are numbers that are much higher or much lower than the rest of the data set and thus, it should not be used when outliers are present.

To illustrate this point, let's look at what happens to the mean when we change 68 to 680. Again, we add the data together: 60 + 72 + 61 + 66 + 63 + 66 + 59 + 64 + 71 + 680 = 1262. Then we take the sum of the data (1262) and divide it by the total number of data (10 girls): 1262 / 10 = 126.2. The mean height (in inches) for the sample of girls is now 126.2. This number is not a good estimate of the central height for the girls. This number is almost twice as high as the height of most of the girls!

However, we can still use other measures of central tendency even when there are outliers. In the scenario above, where a girl who is 680 inches is an outlier, we could use the median. But first, let's explore how to find the median.

The median is the value that cuts the data set in half. If you have an odd number of data, then it's the value that's right in the middle. Let's practice the boys' heights since there are nine boys. There are two steps to finding the median in a sample with an odd number of data:

  1. List the data in numerical order
  2. Locate the value in the middle of the list

Now let's find the median height for our sample of boys. The boys' heights in inches are: 66, 78, 79, 69, 77, 79, 73, 74, 62. So, first we list the data in numerical order: 62, 66, 69, 73, 74, 77, 78, 79, 79. Then, we locate the value in the middle of the list: 62, 66, 69, 73, 74, 77, 78, 79, 79. In a data set that consists of nine items, the datum in the fifth place is the median. The median height for the boys is 74 inches.

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