Question

Fine the lower and upper quartiles and interquetile range.

5, 12, 17, 23, 28, 31, 37, 41, 42, 49, 54, 58, 65, 68, 73, 71.​

Answer 1

Lower Quartile = 25.5

Upper Quartile = 61.5

IQR = 36

Explanation:

Given data is:

5, 12, 17, 23, 28, 31, 37, 41, 42, 49, 54, 58, 65, 68, 73, 71

The lower quartile is the first quartile and upper quartile is the third quartile.

A median divides the data set in two equal halves.

Lower quartile also known as first quartile is the middle value in the first half.

The first half is:

5, 12, 17, 23, 28, 31, 37, 41

As the number of values is even, the quartile will be the average of two middle values

`Q_1 = (23+28)/(2) =(51)/(2)= 25.5`

Upper quartile is the average of middle two values in the second half when the number of values is even.

42, 49, 54, 58, 65, 68, 73, 71

`Q_3 = (58+65)/(2) = (123)/(2) = 61.5`

Interquartile range is the difference of third quartile and first quartile

`IQR = Q_3 - Q_1 = 61.5-25.5=36`

Hence,

Lower Quartile = 25.5

Upper Quartile = 61.5

IQR = 36