Question

If the mean of the data is 60, find the value of $p.$

$\begin{array}{cc}Classmark& frequency\\ 25-35& 12\\ 35-45& 16\\ 45-55& p\\ 55-65& 15\\ 65-75& 8\\ 75-85& 19\\ 85-95& 13\end{array}$

• A. 17

Answer 1

The correct option is A 17

We know that,
$\Rightarrow \text{Mean}=\frac{\sum f_i{x}_i}{\sum f_i}$

Now,
$\begin{array}{ccc}Classmark\left(x_i\right)& Frequency\left(f_i\right)& \left(x_i{f}_i\right)\\ 30& 12& 360\\ 40& 16& 640\\ 50& p& 50p\\ 60& 15& 900\\ 70& 8& 560\\ 80& 19& 1520\\ 90& 13& 1170\end{array}$

So,
$\Rightarrow \sum f_i=83+p$

$\Rightarrow \sum f_i{x}_i=5150+50p$

Now,
$\Rightarrow \frac{\sum f_i{x}_i}{\sum f_i}=\text{Mean}$
$\Rightarrow \frac{5150+50p}{83+p}=60$
$\Rightarrow 5150+50p=4980+60p$
$\Rightarrow 170=10p$
$\Rightarrow p=17$

Hence, the value of p is 17.