Question

Find the mean form the following data:

Find the mean form the following data	No. of Students
Less than 10	5
Less than 20	20
Less than 30	45
Less than 40	70
Less than 50	80
Less than 60	88
Less than 70	98
Less than 80	100

Answer 1

Converting less than cumulative frequency distribution into a simple frequency distribution

Marks	No. of students (c.f)
Less than 10 Less than 20 Less than 30 Less than 40 Less than 50 Less than 60 Less than 70 Less than 80	5 20 45 70 80 88 98 100

Class Interval (Marks)	Mid-Values (m)	Students (f)	fm
0 − 10 10 − 20 20 − 30 30 − 40 40 − 50 50 − 60 60 − 70 70 − 80	5 15 25 35 45 55 65 75	0-5=5 20-5=15 45-20=25 70-45=25 80-70=10 88-80=8 98-88=10 100-98=2	25 225 625 875 450 440 650 150
		Σf=100	Σfm= 3440

Calculating mean from the above data by using direct method:

$$\begin{gathered} \overline{\mathit{X}}=\frac{\Sigma fm}{\Sigma f} \\ or,\overline{X}=\frac{3440}{100} \\ \Rightarrow \overline{X}=34.4\mathrm{marks} \end{gathered}$$

Hence, the mean of the above data is 34.4 marks.