The data set below represents the total number of home runs that a baseball player hit each season for 11 seasons of play. what is the interquartile range of the data?
14, 22, 19, 21, 30, 32, 25, 15, 16, 27, 28
a).12
b).16
c).22
d).28

A. 12

WORKINGS

Given the data set for 11 seasons of play14, 22, 19, 21, 30, 32, 25, 15, 16, 27, 28

Quartiles (usually 3 in number; Q1. Q2 and Q3) divide a rank-ordered data set into four equal parts
14, 22, 19, 21, 30, 32, 25, 15, 16, 27, 28

First order the data set by rank
12, 14, 16, 19, 21, 22, 25, 27, 28, 30, 32

Q1 is the first quartile
Q2 is the second quartile
Q3 is the third quartile
Interquartile range = Q3 – Q1

The median value in the set, Q2 = 22

First half of the rank-ordered data set is therefore 12, 14, 16, 19, 21
While the Second half of the rank-ordered data set is 25, 27, 28, 30, 32

The median value in the first half of the set, Q1 = 16
The median value in the second half of the set, Q3 = 28

Interquartile range = Q3 – Q1
Therefore, interquartile range = 28 – 16
= 12

The interquartile range of the data is 12

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