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.
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