Question

Question 1
Find the mean of the distribution.
$\begin{array}{ccccc}\text{Class}& 1-3& 3-5& 5-7& 7-10\\ \text{Frequency}& 9& 22& 27& 17\end{array}$

Answer 1

We first, find the class mark $x_i$ of each class and then proceed as follows.
$\begin{array}{cccc}\text{Class \& Class marks}\left(x_i\right)& \text{Frequency}\left(f_i\right)& f_i{x}_i& \\ 1-3& 2& 9& 18\\ 3-5& 4& 22& 88\\ 5-7& 6& 27& 162\\ 7-10& 8.5& 17& 144.5\\ & & \sum f_i=75& \sum f_i{x}_i=412.5\end{array}$
Therefore, mean $\left(\overline{x}\right)=\frac{\sum f_i{x}_i}{\sum f_i}=\frac{412.5}{75}=5.5$
Hence, mean of the given distribution is 5.5.