Question

If the mean of 5 observations x, x + 2, x + 4, x + 6 and x + 8 is 11, find the value of x. [CBSE 2014]

Answer 1

Mean of given observations = $\frac{\mathrm{Sum}\mathrm{of}\mathrm{given}\mathrm{observations}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{observations}}$

$$\begin{gathered} \therefore 11=\frac{x+(x+2)+(x+4)+(x+6)+(x+8)}{5} \\ \Rightarrow 55=5x+20 \\ \Rightarrow 5x=55-20 \\ \Rightarrow 5x=35 \\ \Rightarrow x=\frac{35}{5} \\ \Rightarrow x=7 \end{gathered}$$

Hence, the value of x is 7.