Question

In an examination in Hindi, the students of a class secured following marks. Calculate mean marks by Direct Method.

Marks	Number of Students
More than 0 More than 10 More than 20 More than 30 More than 40 More than 50	50 46 40 20 10 5

Answer 1

Converting cumulative frequency Distribution into a simple frequency distribution

Marks	No. of students
0 − 10 10 − 20 20 − 30 30 − 40 40 − 50 50 − 60	50 − 46 = 4 46 − 40 = 6 40 − 20 = 20 20 − 10 = 10 10 − 3 = 7 3 − 0 = 3

Marks	Mid Value (m)	No. of students (f)	Multiple of mid value and frequency (fm)
0 − 10 10 − 20 20 − 30 30 − 40 40 − 50 50 − 60	5 15 25 35 45 55	4 6 20 10 7 3	20 90 500 350 315 165
		Σf = 50	Σfm = 1440

Calculating the mean by Direct method:

$$\begin{gathered} \overline{X}=\frac{\mathrm{\Sigma }fm}{\mathrm{\Sigma }f} \\ \mathrm{or},\overline{X}=\frac{1440}{50} \\ \Rightarrow \overline{X}=28.8 \end{gathered}$$

Hence, the mean marks in Hindi is 28.8