Question

Calculation (i) Arithmetic Mean and (ii) Standard Deviation for the following frequency distribution.

Class Interval	Frequency
20 – 25 25 – 30 30 – 35 35 – 40 40 – 45 45 – 50	8 3 15 12 8 4
	N = 50

Answer 1

Table of calculation
Class Interval	Frequency f	Mid-point X	fX	Deviation	Square of Deviation D2	f.D2
20 – 25	8	22.5	180	–12.1	146.41	1171.28
25 – 30	3	27.5	82.5	– 7.1	50.41	151.23
30 – 35	15	32.5	487.5	– 2.1	4.41	66.15
35 – 40	12	37.5	450	2.9	8.41	100.92
40 – 45	8	42.5	340	7.9	62.41	499.28
45 – 50	4	47.5	190	12.9	166.41	665.64
	= 50		1730			=2654.5

Sum of the frequencies = N = = 50

(i) Mean = = = 34.6

(ii) == = 7.29