Question

If the mean of the following data is 18.75, find the value of p.

$\begin{array}{cccccc}{x}_i& 10& 15& p& 25& 30\\ f_i& 5& 10& 7& 8& 2\end{array}$
[4 MARKS]

Answer 1

Concept: 2 Marks
Application: 2 Marks

We may prepare th frequency table as given below:

$\begin{array}{ccc}{x}_i& f_i& f_i\times x_i\\ 10& 5& 50\\ 15& 10& 150\\ p& 7& 7p\\ 25& 8& 200\\ 30& 2& 60\\ & \sum f_i=32& \sum (f_i\times x_i)=(460+7p)\end{array}$

$\therefore mean=\frac{\sum (f_i\times x_i)}{\sum f_i}=\frac{460+7p}{32}$

But, mean = 18.75 (given)

$\therefore \frac{460+7p}{32}=18.75\Rightarrow 460+7p=(18.75\times 32)$

$\Rightarrow (460+7p)=600$

$\Rightarrow 7p=140\Rightarrow p=20$