Question

Calculate the arithmetic mean from the following data:

Marks	Less than 10	Less than 20	Less than 30	Less than 40	Less than 50
No. of Students	5	15	55	75	100

Answer 1

Marks	Mid Value (m)	No. of student (f)	fm
0 − 10 10 − 20 20 − 30 30 − 40 40 − 50	5 15 25 35 45	5 10 40 20 25	25 150 1000 700 1125
		Σf = 100	Σfm = 3000

For the calculation of mean first the given less than series is converted in continuous class intervals as above.

$\overline{\mathit{X}}=\frac{\mathrm{\Sigma }fm}{\mathrm{\Sigma }f}=\frac{3000}{100}=30$
Thus, mean is 30 marks.

Marks	Mid Value (m)	No. of student (f)	$X-\overline{X}$	$f\left(X-\overline{X}\right)$
0 − 10 10 − 20 20 − 30 30 − 40 40 − 50	5 15 25 35 45	5 10 40 20 25	-25 -15 -5 5 15	-125 -150 -200 100 375
		Σf = 100		$\Sigma f\left(X-\overline{X}\right)$ =0