Question

The mean of 8 numbers is 35. If a number is excluded then the mean is reduced by 3. Find the excluded number.

Answer 1

Mean of 8 numbers = 35
Sum of 8 numbers = $35\times 8=280$
Let the excluded number be x.
Now,
New mean = 35 $-$ 3 = 32
Thus, we have:

$$\begin{gathered} \frac{\mathrm{Sum}\mathrm{of}8\mathrm{numbers}-x}{7}=32 \\ \Rightarrow \frac{280-x}{7}=32 \\ \Rightarrow 280-x=224 \\ \Rightarrow x=56 \end{gathered}$$

Therefore, the excluded number is 56.