Question Video: Finding the Difference between the Medians of Two Data Sets | Nagwa Question Video: Finding the Difference between the Medians of Two Data Sets | Nagwa

# Question Video: Finding the Difference between the Medians of Two Data Sets Mathematics • First Year of Preparatory School

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The table records the heights, in inches, of a group of fifth graders and a group of sixth graders. What is the difference between the medians of the heights of both groups?

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### Video Transcript

The table records the heights, in inches, of a group of fifth graders and a group of sixth graders. What is the difference between the medians of the heights of both groups?

In the table, we have the heights of the fifth graders as 65, 61, 59, 50, 61, 65, and 54 inches. The heights of the sixth graders are 60, 58, 65, 64, 53, 55, and 64 inches. We are asked to find the difference between the median heights of these groups. And we can recall that the median of a set of data is the middle value when the data is given in order, either an ascending or descending order. Because we need to find the difference, we’ll first need to find the medians of each group.

Let’s start by putting the heights of the fifth graders in an ascending order. The smallest height is 50 inches, next 54 inches, and then we have 59, 61, 61, 65, and 65 inches. Even though we have some repeated values, we still record every instance of that same value.

There are seven values in the row for the fifth graders and seven data values in order. The median lies at the middle position. This will be the fourth number in the list. So the median height of the fifth graders is 61 inches.

We can do the same for the sixth graders, starting with putting their heights in an ascending order. The lowest value, or smallest height, is 53 inches. And then we can list the remaining values in ascending order as 55, 58, 60, 64, 64, and 65 inches. Once again, we had the heights of seven sixth graders. So the median will again be at the middle position of the fourth value, which means that the median height of the sixth graders is 60 inches.

To find the difference then, we subtract the smaller value of 60 from the larger value of 61, which gives us the answer that the difference between the median height of these two groups is one inch.

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