What is the interquartile range of the data set: 9, 30, 2, 48, 42, 18, 81, 5, 55, 73, 11?

Interquartile range is ##46##

Interquartile range measures variability, based on difference between third quartile and first quartile. It is defined as ##Q_3-Q_1##.

To find first and third quartile, we should first arrange the data ##{9,30,2,48,42,18,81,5,55,73,11}## in increasing order which is as follows.

##{2,5,9,11,18,30,42,48,55,73,81}##

As there are ##11## data points, ##Q_1## is ##(11+1)/4## or ##3^(rd)## data point i.e. ##9##.

and ##(11+1)xx3/4=9^(th)## data point i.e. ##55##

Hence Interquartile range is ##55-9=46##