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

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.