Question

The mean of the following distribution is 50.
$\begin{array}{cccccc}\text{x}& 10& 30& 50& 70& 90\\ \text{f}& 17& 5a+3& 32& 7a-11& 19\end{array}$
Find the value of a and hence the frequencies of 30 and 70.

Answer 1

We know that,
Mean =$\frac{\sum x_i{f}_i}{\sum f_i}$

Mean
= $\frac{10\times 17+30\times (5a+3)+50\times 32+70\times (7a-11)+90\times 19}{(17+5a+3+32+7a-11+19)}$
⇒$50=\frac{170+150a+90+1600+490a-770+1710}{(60+12a)}$
⇒$40a=200$

⇒$a=\frac{200}{40}$

⇒$a=5$
Hence, the value of a is 5.
Also, the frequency of 30 is 28 and the frequency of 70 is 24.