Question

The mean of 1, 3, 4, 5, 7, 4 is m. The numbers 3, 2, 2, 4, 3, 3, p have mean m − 1 and median q. Then, p + q =

(a) 4
(b) 5
(c) 6
(d) 7

Answer 1

Consider the numbers 3, 2, 2, 4, 3, 3, p.

Mean = $\frac{3+2+3+4+3+3+p}{7}$

$$\begin{gathered} \Rightarrow 7\times \left(4-1\right)=17+p \\ \Rightarrow 21=17+p \\ \Rightarrow p=4 \end{gathered}$$

Arranging the numbers 3, 2, 2, 4, 3, 3, 4 in ascending order, we have

2, 2, 3, 3, 3, 4, 4


∴ q = 3

So,

Hence, the correct option is (d).