Here are some summary statistics for all of the runners in a local 12 kilometre race: slowest $\text { time } = 121$ minutes $\text { mean } = 76$ minutes $\text { median } = 76$ minutes $\text { range } = 91$ minutes $\mathrm { IQR } = 57$ $\mathrm { Q } 1 = 30$ standard $\text { deviation } = 13$ minutes
Between what two values are the middle 50% of times?
A)30 and 87
B)38 and 76
C)15.2 and 60.8
D)19 and 57
E)121 and 30

Question

Quizplus · Accepted Answer

The middle 50% of times are represented by the interquartile range (IQR), which is the difference between the third quartile ($Q3$) and the first quartile ($Q1$). Given $IQR = 57$ and $Q1 = 30$, the third quartile $Q3$ can be calculated as $Q1 + IQR = 30 + 57 = 87$. Therefore, the middle 50% of times are between 30 and 87 minutes.

Here Are Some Summary Statistics for All of the Runners time =121\text { time } = 121 time =121

Here Are Some Summary Statistics for All of the Runners $\text { time } = 121$