Question

Given the data set 62 , 65 , 68 , 70 , 72 , 74 , 76 , 78 , 80 , 82 , 96 , 101, find a) the median, b) the first quartile, c) the third quartile, c) the interquartile range (IQR).

Answer 1

First to sort the data set in ascending order of magnitude :

62 , 65 , 68 , 70 , 72 , 74 , 76 , 78 , 80 , 82 , 96 , 101

number of data points = 12

a) To find Median,

(12/2) = 6th value in the sorted data set = 74

(12/2) +1 = 7th value in the sorted data set = 76

Median

b) To find the first quartile,

(12/4) = 3rd value in the sorted data set = 68

So, Q₁ = 68

c) To find the third quartile,

(12 *3/4) = 9th value in the sorted data set = 80

So, Q₃ = 80

c) The interquartile range (IQR) = Q₃ - Q₁ = 80 - 68 = 12