Question

Mean value of the weekly income of 40 families is 265. But in the calculation, income of one family was read as 150 instead of 115. Find the "Corrected" mean.

Answer 1

Given:
Mean ,$\overline{X}$ = 265
Number of observations, N=40
Incorrect observation = 150
Correct observation = 115

$$\begin{gathered} {\left(\overline{X}\right)}_{Wrong}=\frac{\Sigma X}{N} \\ \mathrm{or},\mathrm{\Sigma }\mathrm{X}=\left(\overline{\mathrm{X}}\right) \end{gathered}$$_Wrong ×N or, ΣX = 265 ×40 = 10,600

Thus, wrong summation X, i.e., ${\left(\Sigma X\right)}_{wrong}$ is 10,600.
Now, correct mean is calculated using the following formula.
$$\begin{gathered} Correct\overline{X}=\frac{\Sigma X_{\left(wrong\right)}+correctvalue-incorrectvalue}{N} \\ \mathrm{Substituting}\mathrm{the}\mathrm{given}\mathrm{values}\mathrm{in}\mathrm{the}\mathrm{formula}. \\ Correct\overline{X}=\frac{10600+115-150}{40} \\ =\frac{10565}{40}=264.125 \end{gathered}$$
Hence, the correct mean is 264.125