Question

Calculate arithmetic mean from the following data:

$\begin{array}{cccccc}\text{Marks}& 0-10& 10-20& 20-40& 40-70& 70-100\\ \text{No. of Students}& 8& 12& 30& 6& 4\end{array}$

Answer 1

In the given example, the class-intervals are unequal. Mean will be calculated directly after calculating the mid-points.

$\begin{array}{cccc}\text{Marks}& \text{Mid-value(m)}& \text{No. of students}& \text{fm}\\ 0-10& 5& 8& 40\\ 10-20& 15& 12& 180\\ 20-40& 30& 30& 900\\ 40-70& 55& 6& 330\\ 70-100& 85& 4& 340\\ & & \sum f=60& \sum fm=1,790\end{array}$

Average Marks $\left(\overline{X}\right)=\frac{\sum fm}{\sum f}=\frac{1,790}{60}=29.83\text{Marks}$

Average marks = 29.83 Marks.