Question

Consider the following data set 20 23 27 21 25 21 24 17 12 28 21 23 12 a) Determine the quartiles for this data. b) Determine the interquartile range for this data. a) The first quartile is the second quartile is □, and the third quartile is (Type integers or decimals.)

Answer 1

Given data values in ascending order as follows:

12, 12, 17, 20, 21, 21, 21, 23, 23, 24, 25, 27, 28

a) Here, 2nd quartile = median = 7th value = 21

1st quartile is median of lower half of median is,

( 17 + 20)/2 = 37/2 = 18.5

and 3rd quartile is median of upper half of median is,

( 24 + 25)/2 = 49/2 = 24.5

Therefore, the first quartile is 18.5, the second quartile is 21, and the third quartile is 24.5

b) IQR = third quartile - first quartile = 24.5 - 18.5 = 6

Therefore, the interquartile range is 6