Question

The mean of 2, 7, 6 and x is 15 and the mean of 18, 1, 6, x and y is 10. What is the value of y?

(a) 5
(b) 10
(c) 20
(d) 30

Answer 1

$$\begin{gathered} \mathrm{Mean}=\frac{\mathrm{Sum}\mathrm{of}\mathrm{observations}}{\mathrm{Number}\mathrm{of}\mathrm{observations}} \\ \Rightarrow 15=\frac{2+7+6+x}{4} \\ \Rightarrow 60=15+x \\ \Rightarrow x=45....\left(1\right) \end{gathered}$$

Now,

$$\begin{gathered} \mathrm{Mean}=\frac{\mathrm{Sum}\mathrm{of}\mathrm{observations}}{\mathrm{Number}\mathrm{of}\mathrm{observations}} \\ \Rightarrow 10=\frac{18+1+6+x+y}{5} \\ \Rightarrow 50=25+x+y \\ \Rightarrow y=25-x \\ \Rightarrow y=25-45\left[\mathrm{From}\left(1\right)\right] \\ \Rightarrow y=-20 \end{gathered}$$

Disclaimer : There is a misprinting in the question. If the mean of 2, 7, 6 and x is 15 then the value of y be −20 and if the mean of 2, 7, 6 and x is 5 then the value of y be 20. So, the correct answer is option (c).