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.
