Question

Consider the following 8 numbers, where one labelled

x
is unknown.

33
,


11
,


5
,


x
,


40
,


46
,


24
,


36


Given that the range of the numbers is 57, work out 2 values of
x
.

Answer 1

x = -11

x = 62

Explanation:

Given:

• Data set: 33, 11, 5, x, 40, 46, 24, 36
• Range: 57

The range of a data set is the difference between its highest and lowest values.

The highest value of the given data set (excluding x) is 46.

The lowest value of the given data set (excluding x) is 5.

The difference between the highest and lowest values is:

⇒ 46 - 5 = 41

As the range is 57, x must be the actual highest or lowest value.

To find the value of x that makes it the lowest value of the data set, subtract the given range from the highest observed value of the data set:

⇒ x = 46 - 57 = -11

To find the value of x that makes it the highest value of the data set, add the given range to the lowest observed value of the data set:

⇒ x = 5 + 57 = 62

Therefore, the two values of x are -11 and 62.