Question

If the mean of 9, 10, 15, x, 6, 8 and 12 is 11. The median of the observations is

(a) 4 (b) 10 (c) 13 (d) 5

Answer 1

The mean of 9, 10, 15, x, 6, 8 and 12 is 11.
$$\begin{gathered} \therefore \mathrm{Mean}=\frac{\mathrm{Sum}\mathrm{of}\mathrm{observations}}{\mathrm{Number}\mathrm{of}\mathrm{observations}} \\ \Rightarrow 11=\frac{9+10+15+x+6+8+12}{7} \\ \Rightarrow x+60=77 \\ \Rightarrow x=77-60=17 \end{gathered}$$
So, the observations are 9, 10, 15, 17, 6, 8 and 12.
Arranging the the observations in increasing order, we get
9, 10, 15, 17, 6, 8, 12 or 6, 8, 9, 10, 12, 15, 17
Thus, the median is 10.
Hence, the correct option is (b).