Question

Find the mean from the following data:

Marks	No. of Students
Above 0	80
Above 10	77
Above 20	72
Above 30	65
Above 40	55
Above 50	43
Above 60	28
Above 70	16
Above 80	10
Above 90	8
Above 100	0

Answer 1

Marks	Students
Above 0 Above 10 Above 20 Above 30 Above 40 Above 50 Above 60 Above 70 Above 80 Above 90 Above 100	80 77 72 65 55 43 28 16 10 8 0

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 80 − 90 90 − 100 100 − 110	5 15 25 35 45 55 65 75 85 95 105	80−77=3 77−72=5 72−-65=7 65−55=10 55−43=12 43−28=15 28−16=12 16−10=6 10−8=2 8−0=8 0−0=0	15 75 175 350 540 825 780 450 170 760 0
		Σf= 80	Σfm= 4140

Calculating mean marks by using direct method:

$$\begin{gathered} \overline{\mathit{X}}=\frac{\Sigma fm}{\Sigma f} \\ or,\overline{X}=\frac{4140}{80} \\ \Rightarrow \overline{X}=51.75m\mathrm{arks} \end{gathered}$$