Question

The following data give the annual salaries (in thousand dollars) of 20 randomly selected health care workers. 50 72 56 38 46 65 37 51 34 62 73 40 68 44 76 61 57 55 65 58 a. Calculate the values of the three quartiles and the interquartile range.

Answer 1

So, the interquartile range is IQR=22.5.

Explanation:

Let us write the numbers in ascending order:

34, 37, 38, 40, 44, | 46, 50, 51, 55, 56, |

57, 61, 62, 65, 65, | 68, 68, 72, 73, 76.

We calculate quartile 1:

`Q_1=(44+46)/(2)=45`

We calculate quartile 2:

`Q_2=(56+57)/(2)=56.5\\`

We calculate quartile 3:

`Q_3=(65+68)/(2)=67.5\\`

We calculate the interquartile range:

`IQR=Q_3-Q_1\\\\IQR=67.5-45\\\\IQR=22.5`