Question

The mean of the marks scored by 50 students was found to be 39. Later on it was discovered that a score of 43 was misread as 23. Find the correct mean.

Answer 1

Let the marks scored by 50 students be x₁, x₂,...x₅₀.
Mean = 39
We know:
$\mathrm{Mean}=\frac{\mathrm{Sum}\mathrm{of}\mathrm{observa}\mathrm{tions}}{\mathrm{Number}\mathrm{of}\mathrm{observations}}$

Thus, we have:

$$\begin{gathered} 39=\frac{x_1+x_2+...+x_{50}}{50} \\ \Rightarrow x \end{gathered}$$
_{$\Rightarrow x_1+x_2+....+x_{50}=1950......\left(\mathrm{i}\right)$}

Also, a score of 43 was misread as 23.
$$\begin{gathered} \therefore \mathrm{New}\mathrm{Mean}=\frac{\left(x_1+x_2+...+x_{50}\right)-23+43}{50} \\ =\frac{1950-23+43}{50}\left[\mathrm{using}\left(\mathrm{i}\right)\right] \\ =\frac{1970}{50} \\ =39.4 \end{gathered}$$