Question

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

Answer 1

The range is 39

The interquartile range is 32

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 $Q_3$

$Q_2=72$

$Q_1=\frac{57+63}{2} =60$

$Q_3=\frac{88+96}{2} =92$

Interquartile range = $Q_3-Q_1$

                               =  $92-60$

                               =  $32$

The interquartile range is 32

Answer 2

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