Based on the calculations, the interquartile range of a data set is equal to 53.
In order to determine the statistical measures or the five-number summary, we would arrange the data set in an ascending order:
6,8,9, 30, 30, 36, 38, 54, 64, 70, 75, 81, 93
Based on the data set, the first quartile can be calculated as follows;
First quartile = [(n + 1)/4]th term
First quartile = (13 + 1)/4
First quartile = 3.5th term
First quartile = (30+9)/2
First quartile = 19.5.
For the third quartile, we have:
Third quartile = [3(n + 1)/4]th term
Third quartile = 3 × 3.5th term
Third quartile = 10.5th term
Third quartile = (75+70)/2
Third quartile = 72.5
Mathematically, the interquartile range of a data set is the difference between third quartile (Q₃) and the first quartile:
Interquartile range of data set = Third quartile - First quartile
Interquartile range of data set = 72.5 - 19.5
Interquartile range of data set = 53.