Question

The mean salary paid to 1000 workers of a factory was found to be ₹ 180.4 . Later on it was discovered that the wages of two workers were wrongly taken as 297 and 165 instead of 197 and 185. Find the correct mean.

Answer 1

Given:
Number of workers = 1000
Incorrect values = 297, 165
Correct values = 197, 185
Incorrect mean = 180.4

$$\begin{gathered} \mathrm{Incorrect}\mathrm{Mean},{\overline{X}}_{\mathrm{I}}=\frac{\Sigma X_{\mathrm{I}}}{N} \\ 180.4=\frac{\Sigma X_{\mathrm{I}}}{1000} \\ \Sigma X_{\mathrm{I}}=180400 \end{gathered}$$

Correct ΣX_C =ΣX_I + correct values - incorrect values
= ΣX_I + 197 + 185 − 297 − 165
= 180400 + 197 + 185 − 297 − 165
= 180320
$\mathrm{Correct}\overline{X}=\frac{\Sigma X_{\mathrm{C}}}{N}=\frac{180320}{1000}=180.32$
Thus, the correct mean wage is Rs 180.32.