Question

The average height of a group of 40 students was calculated as 155 cm. It was later discovered that the height of one student was read as 157 instead of 137 cm. Calculate the correct average height.

Answer 1

Given:

Mean, $\overline{\mathbf{X}}$= 155
Number of observations =40
Incorrect observation= 157
Correct Observation = 137

$$\begin{gathered} {\overline{\mathrm{X}}}_{wrong}=\frac{\Sigma X_{wrong}}{N} \\ or,155=\frac{\Sigma X_{wrong}}{40} \\ or,\Sigma X_{wrong}=155\times 40 \\ \Rightarrow \Sigma X_{wrong}=6200 \end{gathered}$$

Thus, wrong summation of X, i.e., $\mathit{\Sigma }{\mathit{X}}_{\mathbf{\left(}\mathbf{w}\mathbf{r}\mathbf{o}\mathbf{n}\mathbf{g}\mathbf{\right)}}$ is 6200
Now, correct mean is calculated using the following method.

$$\begin{gathered} \mathrm{Correct}\overline{X}=\frac{\Sigma X_{wrong}+\mathrm{correct}\mathrm{value}-\mathrm{incorrect}\mathrm{value}}{N} \\ \mathrm{Substituting}\mathrm{the}\mathrm{given}\mathrm{values}\mathrm{in}\mathrm{the}\mathrm{formula}. \\ \mathrm{Correct}\overline{\mathrm{X}}=\frac{6200+137-157}{40} \\ \mathrm{or},\mathrm{Correct}\overline{\mathrm{X}}=\frac{6180}{40} \\ \Rightarrow \mathrm{Correct}\overline{\mathrm{X}}=154.5 \end{gathered}$$

Hence, the correct average height is 154.5 cm