Question

The mean of 100 items was found to be 64. Later on it was discovered that two items were misread as 26 and 9 instead of 36 and 90 respectively. Find the correct mean.

Answer 1

Let the items be x₁, x₂,...x₁₀₀
Given:
Mean = 64
We know:

$\mathrm{Mean}=\frac{\mathrm{Sum}\mathrm{of}\mathrm{observa}\mathrm{tions}}{\mathrm{Number}\mathrm{of}\mathrm{observations}}$

$$\begin{gathered} \mathrm{Thus},\mathrm{we}\mathrm{have}: \\ 64=\frac{x_1+x_2+...+x_{100}}{100} \end{gathered}$$

_{$\Rightarrow x_1+x_2+.......+\hspace{0.17em}{x}_{100}=6400$}


Because items 36 and 90 were misread as 26 and 9, we have:

Correct Mean = $\frac{\left(x_1+x_2+.......+x_{100}\right)-(26+9)+(36+90)}{100}$
$$\begin{gathered} =\frac{6400-35+126}{100} \\ =\frac{6491}{100} \\ =64.91 \end{gathered}$$