Answer:
Set B has a greater spread , because it has a higher IQR
Explanation:
One way to measure the spread of a data set is to break it into quarters and measure the interquartile range (IQR).
Set A: {38, 12, 23, 48, 55, 16, 18}
(a) Sort the numbers
(12, 16, 18, 23, 38, 48, 55}
(b) First quartile
The median of 12, 16, and18 is 16.
First quartile = 16
(c) Third quartile
The median of 38, 48, and 55 is 48.
Third quartile = 48
(d) IQR
IQR = 48 - 16 = 32
Set B: {44, 13, 24, 12, 56}
(a) Sort the numbers
(12, 13, 24, 44, 56}
(b) First quartile
The median of 12 and 13 is 12.5.
First quartile = 12.5
(c) Third quartile
The median of 44 and 56 is 50.
Third quartile = 50
(d) IQR
IQR = 50 - 12.5 = 37.5
Set B has the greater spread, because it has the higher IQR.
The Box plot below shows that Set B has the greater spread.