Question

The heights of 10 students, measured in cm are as follows:
143, 132, 150, 139, x, 135, 151, 146, 141, 149
If the mean of the given data is 138 and x < 132, then find the range of the given data.

• A. 40 cm
• B. 31 cm
• C. 57 cm
• D. 82 cm

Answer 1

The correct option is C 57 cm

Descending order of the data is,
151, 150, 149,146, 143, 141, 139, 135, 132, x

Given: Mean = 138 and x< 132.

$\Rightarrow$ x is the smallest value in the given set of values.

Range is the difference between highest value and lowest value.
$\Rightarrow$ Range = 151 - x

Now, we need to find x first.

Mean of the given data
$=\frac{Sumofalltheobservations}{Totalnumberofobservations}$

$\Rightarrow 138=\frac{143+132+150+139+x+135+151+146+141+149}{10}$

$\Rightarrow 138=\frac{1286+x}{10}$

$\Rightarrow 1286+x=1380$

$\Rightarrow x=1380-1286=94$

Therefore, range = 151 - x = 151 - 94 = 57 cm