Question

Find the mean of the following data by assumed mean method.
$\begin{array}{cc}ClassInterval& Frequency\\ 2-8& 6\\ 8-14& 3\\ 14-20& 12\\ 20-26& 11\\ 26-32& 8\end{array}$

• A. 17.8
• B. 18.8
• C. 16.2
• D. 16.1

Answer 1

The correct option is B 18.8

Let the assumed mean 'a' be 17

$\begin{array}{ccccc}ClassInterval& f_i& x_i& d_i=x_i-a& f_i{d}_i\\ 2-8& 6& 5& -12& -72\\ 8-14& 3& 11& -6& -18\\ 14-20& 12& 17=a& 0& 0\\ 20-26& 11& 23& 6& 66\\ 26-32& 8& 29& 12& 96\end{array}$

Here,

$\sum f_i=40$

$\sum f_i{d}_i=72$

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

$=17+\frac{72}{40}=17+1.8=18.8$

$\therefore$ The mean of the data is 18.8