Question

The table below shows the number of hours some college athletes in two states spend on indoor sports each week:

State A79542521668
State B141210131514111516


Part A: Create a five-number summary and calculate the interquartile range for the two sets of data.

Answer 1

State A: 7 9 5 4 25 21 6 6 8
State B: 14 12 10 13 15 14 11 15 16

When arranged in order,
State A: 4 5 6 6 7 8 9 21 25
State B: 10 11 12 13 14 14 15 15 16

Part A:
For state A, Q1 = minimum number = 4, Q2 is the lower quartile = 6, Q3 is the middle number = 7, Q4 is the upper quartile = (9 + 21)/2 = 15, Q5 = maximum number = 25
Interquatile range = upper quatile - lower quatile = 15 - 6 = 9

For state B, Q1 = minimum number = 10, Q2 is the lower quartile = 11.5, Q3 is the middle number = 14, Q4 is the upper quartile = 15, Q5 = maximum number = 16
Interquatile range = upper quatile - lower quatile = 15 - 11.5 = 3.5