Question

If the mean of the following frequency distribution is $7.5,$ find the missing frequency $f.$

$\begin{array}{ccccccccc}Variable& 5& 6& 7& 8& 9& 10& 11& 12\\ Frequency& 20& 17& f& 10& 8& 6& 7& 6\end{array}$

Answer 1

We construct the following table:

$\begin{array}{ccc}Variable& Frequency& Product\\ x& y& xy\\ 5& 20& 100\\ 6& 17& 102\\ 7& f& 7f\\ 8& 10& 80\\ 9& 8& 72\\ 10& 6& 60\\ 11& 7& 77\\ 12& 6& 72\\ Total& \sum y=74+f& \sum xy=563+7f\end{array}$

$\therefore Mean=\frac{\sum xy}{\sum y}$

$\Rightarrow 7.5=\frac{563+7f}{74+f}$

$\Rightarrow 555+7.5f=563+7f$

$\Rightarrow 7.5f-7f=563-555$

$\Rightarrow 0.5f=8$

$\Rightarrow f=\frac{8}{0.5}=16$