Question

The heights of the players on the boys' basketball team in inches are as follows:

78, 73, 75, 70, 72, 71, 73, and 76.

The heights of the players on the girls' basketball team in inches are as follows:

72, 68, 66, 68, 66, 65, and 70.

What is the difference between the median boys' height and the median girls' height?

answers below:

4 in.

6 in.

5 in.

7 in.

Answer 1

To find the difference between the median heights of the boys' and girls' basketball teams, we first need to calculate the medians for both sets of measurements.

**Boys' Heights:**
The heights are:
78, 73, 75, 70, 72, 71, 73, and 76.

First, sort the heights in ascending order:
70, 71, 72, 73, 73, 75, 76, 78.

Since there are 8 heights (an even number), the median is the average of the two middle numbers. The two middle numbers are the 4th and 5th heights:
73 and 73.

Calculating the median:
\[
\text{Median boys' height} = \frac{73 + 73}{2} = 73.
\]

**Girls' Heights:**
The heights are:
72, 68, 66, 68, 66, 65, and 70.

First, sort the heights in ascending order:
65, 66, 66, 68, 68, 70, 72.

Since there are 7 heights (an odd number), the median is the middle number, which is the 4th height:
68.

Now we have both medians:
- Median boys' height = 73
- Median girls' height = 68

To find the difference, we subtract the median girls' height from the median boys' height:
\[
73 - 68 = 5.
\]

Thus, the difference between the median boys' height and the median girls' height is \( \boxed{5} \) inches.