Question

If the arithmetic mean, 7, 8, x, 11, 14 is x, then x =

(a) 9
(b) 9.5
(c) 10
(d) 10.5

Answer 1

The given observations are 7, 8, x, 11, 14.

Mean = x (Given)

Now,

$$\begin{gathered} \mathrm{Mean}=\frac{7+8+x+11+14}{5} \\ \Rightarrow x=\frac{40+x}{5} \\ \Rightarrow 5x=40+x \\ \Rightarrow 4x=40 \\ \Rightarrow x=10 \end{gathered}$$

Hence, the correct option is (c).