Here is the five-number summary for a group of 100 runners in a 5-kilometer race. the variable is the time to complete the race. five-number summary: minimum: 15 minutes q1: 27 minutes median: 31 minutes q3: 32 minutes maximum: 50 minutes are there any outliers in the runners' finish times by the 1.5 * iqr definition?

Given:

Minimum = 15 min

Q1 = 27 min, the 25 quartile

Q2 = 31 min, the median

Q3 = 32 min, the 75% quartile

Maximum = 50 min

Calculate the IQR (Inter quartile range).

IQR = Q3 - Q1 = 32 - 27 = 5

To detect outliers, use the k = 1.5 test.

The expected range is

[Q1 - 1.5*IQR, Q3 + 1.5*IQR]

= [27 - 1.5*5, 32 + 1.5*5]

= [19.5, 39.5]

The actual range is [15, 50].

The minimum is less than 19.5.

The maximum is greater than 39.5

Therefore outliers exist.

Answer: There are outliers.