Question

Calculate the Mean of the distribution given using Assumed mean Method.

$\begin{array}{cc}\text{Marks}& \text{No. of Students}\\ 10-20& 2\\ 20-30& 6\\ 30-40& 10\\ 40-50& 12\\ 50-60& 9\\ 60-70& 8\\ 70-80& 4\\ 80-90& 3\end{array}$

• A. 52.11
• B. 55
• C. 48.89
• D. 46.5

Answer 1

The correct option is C 48.89

$\begin{array}{ccccc}\text{Classes}& \text{Class marks (x)}& d=x-a& \text{Frequency (f)}& fd\\ 10-20& 15& -40& 2& -80\\ 20-30& 25& -30& 6& -180\\ 30-40& 35& -20& 10& -200\\ 40-50& 45& -10& 12& -120\\ 50-60& 55& 0& 9& 0\\ 60-70& 65& 10& 8& 80\\ 70-80& 75& 20& 4& 80\\ 80-90& 85& 30& 3& 90\\ & & \sum d=-40& \sum f=54& \sum fd=330\end{array}$

Let, the assumed mean 'a' = 55

$\therefore \text{Mean}=a+\frac{\sum fd}{\sum f}$

$=55+\frac{-330}{54}=55-6.11=48.89$