Question

The average weight of a group of 20 boys was calculated to be 89.4. It was later discovered that one weight was misread as 78 kg instead of the correct on of 87 kg. Calculate the correct average weight.

Answer 1

Given:

Mean, $\overline{\mathbf{X}}$=89.4
Number of observations, N=20
Incorrect observation= 78
Correct observation = 87

$$\begin{gathered} \mathrm{Wrong}\overline{\mathrm{X}}=\frac{\mathrm{Wrong}\mathrm{\Sigma X}}{N} \\ or,89.4=\frac{\mathrm{Wrong}\mathrm{\Sigma X}}{20} \\ \Rightarrow \mathrm{Wrong}\mathrm{\Sigma X}=1788 \end{gathered}$$

Thus, wrong summation of X, i.e., ${\left(\Sigma X\right)}_{wrong}$ is 1788.
Now, Correct mean is calculated using the following formula.

$$\begin{gathered} \mathrm{Correct}\overline{X}=\frac{\Sigma X_{\left(wrong\right)}+\mathrm{corrected}\mathrm{value}-\mathrm{incorrect}\mathrm{value}}{N} \\ \mathrm{Substituting}\mathrm{the}\mathrm{given}\mathrm{values}\mathrm{in}\mathrm{the}\mathrm{formula}. \\ \mathrm{Correct}\overline{\mathrm{X}}=\frac{1788-78+87}{20}=\frac{1797}{20}=89.95 \end{gathered}$$

Hence, the correct average weight is 89.95 kgs