The Mean vs the Median: Differences & Uses

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  • 0:02 Mean vs. Median
  • 1:22 Using Mean
  • 3:33 Using Median
  • 5:29 Lesson Summary
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Lesson Transcript
Instructor: Cathryn Jackson

Cat has taught a variety of subjects, including communications, mathematics, and technology. Cat has a master's degree in education and is currently working on her Ph.D.

Most people can find the mean and the median of a data set, but do you know when to use the mean and when to use the median to describe the information?

Mean vs. Median

Paulo is a famous artistic director, and he is casting for a new project that he is directing: Statistics, The Musical. He wants to have all of the chorus members tall and of roughly similar heights. Paulo believes that he can use mathematics to find the information he needs. Paulo can get this information by finding the mean and the median of the heights.

The mean is the sum of the numbers in a data set divided by the total number of values in the data set. The mean is also known as the average. The mean can be used to get an overall idea or picture of the data set. Mean is best used for a data set with numbers that are close together.

The median is the midpoint value of a data set, where the values are arranged in ascending or descending order. The median can be used to get an idea of what values fall above the midpoint and what values fall below the midpoint. There is equal likelihood that the values in the data set will fall either above or below the median. Median is best used for a data set with numbers that have a few larger or smaller numbers and have several numbers close together. One large or small number might skew the mean, but the median can often give you a better idea of the data.

Using Mean

Paulo has chorus members audition in two groups. The first group has the following heights, in inches: 68, 73, 69, 68, 71, 69, 70 and 72. The second group has the following heights, in inches: 77, 76, 66, 67, 79, 66, 65 and 64. To find the mean of each group, we will add the numbers in the data set.

68 + 73 + 69 + 68 + 71 + 69 + 70 + 72 = 560

Then we need to count the numbers in the data set. There are eight numbers in this data set. To find the mean, we need to divide the sum, 560, by 8. That gives us an average of 70 inches. Paulo wants a group that has an average of 70 inches. So, it looks like the first group has a great chance at getting the job. Let's find the mean of the second group:

77 + 76 + 66 + 67 + 79 + 66 + 65 + 64= 560/8 = 70

Wow! This group also has an average of 70 inches. How will Paulo decide? Well, assuming that they have equal dancing, singing and acting abilities, let's look at how these two groups look on stage. This group looks like all of the members have a similar height:

The people in this group have similar heights.
group of people of similar height

They look great on stage together.

Let's take a look at the second group:

The people in this group do not have similar heights.
group of people of different heights

Hmmmmm…This group looks a bit strange. Even though the mean height of this group is 70 inches, they don't really look proportional on stage.

Remember that mean is used when the numbers are close together, but median is used for numbers that are far apart. Without looking at the people together on stage, Paulo might have thought that both groups would look the same. Let's find the median of both groups and see if that gives us more helpful information.

Using Median

To find the median, you first need to order the numbers in either ascending or descending order. Let's put the heights of group one in order:

68, 68, 69, 69, 70, 71, 72, 73

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