Question

What is the interquartile range of the data set shown below? 25, 28, 32, 35, 36, 40, 46 (1) 12 (2) 14 (3) 19 (4) 21

Answer 1

1) 12

Step-by-step explanation

The interquartile range is the difference between the third quartile and the first quartile.

The second quartile Q2 is the median of the data set:

`Q_2=(25+28+32+35+36+40+46)/(7)=(242)/(7)=35.57\approx35`

The first quartile Q1 is the median of the first half of the data set, not including Q2: 25, 28, 32:

`Q_1=(25+28+32)/(3)=(85)/(3)=28.333\approx28`

The third quartile is the median of the second half of the data set, not including Q2: 36, 40, 46:

`Q_3=(36+40+46)/(3)=(122)/(3)=40.666\approx40`

The interquartile range IQR is:

`\text{IQR}=Q_3-Q_1=40-28=12`