Question

Find the arithmetic mean of following data by assumed mean method
$\begin{array}{cc}x& f\\ 5& 4\\ 10& 5\\ 15& 7\\ 20& 4\\ 25& 3\\ 30& 2\end{array}$

• A. 15
• B. 14.4
• C. 15.6
• D. 16

Answer 1

The correct option is C 15.6

Let the assumed mean 'a' be 15

$\begin{array}{cccc}{x}_i& f_i& d_i=x_i-a& f_i{d}_i\\ 5& 4& -10& -40\\ 10& 5& -5& -25\\ 15& 7& -0& -0\\ 20& 4& 5& 20\\ 25& 3& 10& 30\\ 30& 2& 15& 30\end{array}$

Here,

$\sum f_i=25$

$\sum f_i{d}_i=15$

$\therefore Mean=a+\frac{\sum f_i{d}_i}{\sum f_i}$

$=15+\frac{15}{25}=15.6$

$\therefore$ The mean of the data is 15.6