Question

ratings for passers in a football league are given. find the interquartile range, where inter - quartile range = q3 - q1.
what is the interquartile range?
passer\trating points
passer 1\t101.6
passer 2\t94.6
passer 3\t92.3
passer 4\t86.5
passer 5\t84.2
passer 6\t80.7
passer 7\t78.9
passer 8\t77.6
passer 9\t76.7
passer 10\t74.8

Explanation:

Step1: Arrange data in ascending order

74.8, 76.7, 77.6, 78.9, 80.7, 84.2, 86.5, 92.3, 94.6, 101.6

Step2: Find the median (Q2)

Since there are 10 data - points, the median is the average of the 5th and 6th ordered values. $Q2=\frac{80.7 + 84.2}{2}=82.45$.

Step3: Find Q1

The lower half of the data is 74.8, 76.7, 77.6, 78.9, 80.7. The median of the lower half (Q1) is the 3rd value, so $Q1 = 77.6$.

Step4: Find Q3

The upper half of the data is 84.2, 86.5, 92.3, 94.6, 101.6. The median of the upper half (Q3) is the 3rd value of the upper - half, so $Q3=92.3$.

Step5: Calculate the inter - quartile range

$IQR = Q3−Q1=92.3 - 77.6 = 14.7$

Answer:

14.7