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 (xi)	No. of students (fi)	ui = xi - A = xi - 25	fiui
5	15	-20	-300
10	50	-15	-750
15	80	-10	-800
20	76	-5	-380
25	72	0	0
35	45	5	225
40	39	10	390
45	9	15	135
45	8	20	160
50	6	25	150
	N = 400		\(\sum\)fiui = -1170

Mean = A + \(\frac{\sum f_iu_i}{N}\)

\(=25+\frac{-1170}{400}=\frac{1000-1170}{400}\)

\(=22.075\)