Question

Question 3
Calculate the mean of the following data
$\begin{array}{ccccc}\text{Class}& 4-7& 8-11& 12-15& 16-19\\ \text{Frequency}& 5& 4& 9& 10\end{array}$

Answer 1

Since, given data is not continuous, so we subtract 0.5 from the lower limit and add 0.5 in the upper limit of each class.
Now, we first find the class mark $x_i$ of each class and then proceed as follows
$\begin{array}{cccc}\text{Class}& Classmarks\left(x_i\right)& \text{Frequency}\left(f_i\right)& f_i{x}_i\\ 3.5-7.5& 5.5& 5& 27.5\\ 7.5-11.5& 9.5& 4& 38\\ 11.5-15.5& 13.5& 9& 121.5\\ 15.5-19.5& 17.5& 10& 175\\ & & \sum f_i=28& \sum f_i{x}_i=362\end{array}$
Therefore, $\overline{x}\left(mean\right)=\frac{\sum f_i{x}_i}{\sum f_i}=\frac{362}{28}=12.93$
Hence, mean of the given data is 12.93.