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
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