Question

Which set of data has the highest interquartile range? Group of answer choices 8,12,14,14,20 8,12,14,14,22 9,13,14,15,19 all of the above

Answer 1

Given:

The given data set are:

8,12,14,14,20

8,12,14,14,22

9,13,14,15,19

All of the above

To find:

The set of data that has the highest interquartile range(IQR).

Solution:

We know that, the interquartile range(IQR) of a data set is the difference between the third quartile and first quartile.

`IQR=Q_3-Q_1`

All the given data set has five values in ascending order. So, the first value is the minimum value, second value is the first quartile, third value is the median, the fourth value is the third quartile and the fifth value is the maximum value.

For 8,12,14,14,20,

`IQR=14-12`

`IQR=2`

For 8,12,14,14,22,

`IQR=14-12`

`IQR=2`

For 9,13,14,15,19,

`IQR=15-13`

`IQR=2`

All interquartile ranges are equal. So, all the data sets has t he highest interquartile range.

Therefore, the correct option is D.