Question

Fine the lower and upper quartiles and interquetile range.

Answer 1

Answer:

Lower Quartile = 25.5

Upper Quartile = 61.5

IQR = 36

Step-by-step 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

$Q_1 = \frac{23+28}{2} =\frac{51}{2}= 25.5$

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

$Q_3 = \frac{58+65}{2} = \frac{123}{2} = 61.5$

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