Question

If the mean of the following frequency distribution is 4.5, find the misssing frequency f.

$\begin{array}{ccccccccccc}\text{Variable}& 1& 2& 3& 4& 5& 6& 7& 8& 9& 10\\ \text{Frequency}& 5& 12& \text{f}& 13& 7& 9& 12& 3& 11& 4\end{array}$

• A. 25
• B. 50
• C. 35
• D. 60

Answer 1

The correct option is B 50

$\begin{array}{ccc}\text{Variable}& \text{Frequency}& \text{Product}\\ x& y& xy\\ 1& 5& 5\\ 2& 12& 24\\ 3& \text{f}& 3\text{f}\\ 4& 13& 52\\ 5& 7& 35\\ 6& 9& 54\\ 7& 12& 84\\ 8& 3& 24\\ 9& 11& 99\\ 10& 4& 40\\ \text{Total}& \sum y=76+\text{f}& \sum xy=417+3\text{f}\end{array}$

Mean = $\frac{\Sigma xy}{\Sigma y}$

$\Rightarrow 4.5=\frac{417+3f}{76+f}$

$\Rightarrow 342+4.5f=417+3f$

$\Rightarrow 4.5f-3f=417-342$

$\Rightarrow 1.5f=75$

$\Rightarrow f=\frac{75}{1.5}=50$