Question

Find the range and the interquartile range.
57,96,72,63,88

Answer 1

List the data set from least to greatest:

57, 63, 72, 88, 96

Range: Highest value - Lowest value = answer

Range: 96 - 57 = 39

(IQR) Interquartile Range: Upper quartile - Lower quartile = answer

(IQR) Interquartile range: 88.5 - 57.5 = 31

Answer 2

The range is 39

The interquartile range is 32

Step-by-step explanation:

The given data is
`57,96,72,63,88`

Let us arrange the data in ascending order.

Thus, we have,

`57,63,72,88,96`

We need to determine the range and interquartile range of the data.

Range:

The range of the data is the difference between the highest and the lowest value in the given data.

Highest value = 96

Lowest value = 57

Range = Highest value - Lowest value

= 96 - 57

= 39

Thus, the range of the data is 39

Interquartile range:

The interquartile range is the difference between the upper quartile and the lower quartile in the given data.

From, the given data, we have, 3 quartiles. They are
`Q_1 , Q_2` and
`Q_3`

`Q_2=72`

`Q_1=(57+63)/(2) =60`

`Q_3=(88+96)/(2) =92`

Interquartile range =
`Q_3-Q_1`

=
`92-60`

=
`32`

The interquartile range is 32