Question

The mean of 10, 15, 19, 30, 43, 69 and x is x. Then the median is

(a) 19 (b) 43 (c) 30 (d) None of these

Answer 1

The mean of 10, 15, 19, 30, 43, 69 and x is x.
$$\begin{gathered} \therefore \mathrm{Mean}=\frac{\mathrm{Sum}\mathrm{of}\mathrm{observations}}{\mathrm{Number}\mathrm{of}\mathrm{observations}} \\ \Rightarrow x=\frac{10+15+19+30+43+69+x}{7} \\ \Rightarrow x+186=7x \\ \Rightarrow x=\frac{186}{6}=31 \end{gathered}$$
Thus, the observations are 10, 15, 19, 30, 43, 69 and 31.
Arranging the numbers 10, 15, 19, 30, 43, 69 and 31 in increasing order, we get
10, 15, 19, 30, 31, 43, 69
Thus, the median is 30.
Hence, the correct option is (c).