Question

Find the mi9ssing frequency from the followinjg table:

Marks	No. of Students
Below 10	25
Below 20	40
Below 30	60
Below 40	75
Below 50	95
Below 60	125
Below 70	190
Below 80	240

Answer 1

Marks	Students
Below 10 Below 20 Below 30 Below 40 Below 50 Below 60 Below 70 Below 80	25 40 60 75 95 125 190 240

Class Interval	Mid-Values (m)	No. of 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	25-0=25 40-25=15 60-40=20 75-60=15 95-75=20 125-95=30 190-125=65 240-190=50	125 225 500 525 900 1650 4225 3750
		$\mathit{\Sigma }\mathit{f}$=240	$\mathit{\Sigma }\mathit{f}\mathit{m}$=11,900

Calculating average marks using direct method:

$$\begin{gathered} \overline{\mathit{X}}=\frac{\Sigma fm}{\Sigma f} \\ or,\overline{X}=\frac{11900}{240} \\ \Rightarrow \overline{X}=49.58\mathrm{marks} \end{gathered}$$

Hence, the average marks are 49.58