What percentage of the general us population have bachelor's degrees? the statistical abstract of the united states (120th edition), gives the percentage of bachelor's degrees by state. for convenience, the data are sorted in increasing order.17, 18, 18, 18, 19, 20, 20, 20, 21, 2121, 21, 22, 22, 22, 22, 22, 22, 23, 2324, 24, 24, 24, 24, 24, 24, 24, 25, 2626, 26, 26, 26, 26, 27, 27, 27, 27, 2728, 28, 29, 31, 31, 32, 32, 34, 35, 38 find the interquartile range

First, we find the first quartile, ,
is the number below which 25% of the data are.

Given the data set:
17, 18, 18, 18, 19, 20, 20, 20, 21, 21, 21, 21, 22, 22, 22, 22, 22, 22, 23, 23, 24, 24, 24, 24, 24, 24, 24, 24, 25, 26, 26, 26, 26, 26, 26, 27, 27, 27, 27, 27, 28, 28, 29, 31, 31, 32, 32, 34, 35, 38

There are 50 numbers in the data set. Dividing the data set into two halves, we have the first half as:
17, 18, 18, 18, 19, 20, 20, 20, 21, 21, 21, 21, 22, 22, 22, 22, 22, 22, 23, 23, 24, 24, 24, 24, 24

Furthe dividing the first half of the data into two gives:
17, 18, 18, 18, 19, 20, 20, 20, 21, 21, 21, 21, | 22, | 22, 22, 22, 22, 22, 23, 23, 24, 24, 24, 24, 24

This gives the number '22' as the middle number and hence, the first quatile.

Doing similar process to the second half of the data gives the number '27' as the middle number and hence the upper quartile, .
is the number above which 25% of the data are.

Interquartile range is given by