Question

Find the mean from the following frequency distribution of marks at a test in statistics:

Marks(x)	5	10	15	20	25	30	35	40	45	50
No. of students (f)	15	50	80	76	72	45	39	9	8	6

Answer 1

Let the assumed mean (A) = 25

Marks (x1)	No. of students (f1)	u1 = x1 - A = x1 - 25	f1u1
5	15	-20	-300
10	50	-15	-750
15	80	-10	-800
20	76	-5	-380
25	72	0	0
30	45	5	225
35	39	10	390
40	9	15	135
45	8	20	160
50	6	25	150
	N = 400		`sumf_1"u"_1=-1170`

Mean `=A+(sumf_1"u"_1)/N`

`=25+(-1170)/400`

`=(10000-1170)/400`

= 22.075