The average height of 30 boys was calculated to be 150 cm.

Question:

The average height of 30 boys was calculated to be 150 cm. It was detected later that one value of 165 cm was wrongly copied as 135 cm for the computation of the mean. Find the correct mean.

Solution:

We know that,

Mean $=\frac{\text { Sum of observa tions }}{\text { Number of observations }}$

Mean of height of 30 boys $=\frac{\sum_{i=1}^{30} x_{i}}{30}$

$\Rightarrow 150=\frac{\sum_{i=1}^{30} x_{i}}{30}$

$\Rightarrow \sum_{i=1}^{30} x_{i}=150 \times 30$

$\Rightarrow \sum_{i=1}^{30} x_{i}=4500 \quad \ldots(1)$

It was detected later that one value of 165 cm was wrongly copied as 135 cm for the computation of the mean.

$\therefore$ The correct mean $=\frac{\sum_{i=1}^{30} x_{i}-135+165}{30}$

$=\frac{\sum_{i=1}^{30} x_{i}+30}{30}$

$=\frac{4500+30}{30}$            (from (1))

$=\frac{4530}{30}$

$=151$

Hence, the correct mean is 151.