Question

Find out the missing item x of the following distribution, where arithmetic mean $\left(\overline{X}\right)$ is 11.37

$\begin{array}{cccccccc}X& 5& 7& X& 11& 13& 16& 20\\ \text{Frequency (f)}& 2& 4& 29& 54& 11& 8& 4\end{array}$

Answer 1

Calculation of Missing Item

$\begin{array}{ccc}X& \text{Frequency (f)}& \text{fx}\\ 5& 2& 10\\ 7& 4& 28\\ x& 29& 29\left(x\right)\\ 11& 54& 594\\ 13& 11& 143\\ 16& 8& 128\\ 20& 4& 80\\ & \sum f=112& \sum fx=983+29x\end{array}$

$\therefore \overline{X}=\frac{\sum fx}{\sum f}$

$\Rightarrow 11.37=\frac{983+29x}{112}$

$\Rightarrow 1273.44=983+29x$

$\Rightarrow 29x=290.44$

$\Rightarrow x=10.01=10$

Hence, the missing value is 10.