Question

Find the Arithmetic Mean of the following data using Step Deviation Method:

Age	15 − 19	20 − 24	25 − 29	30 − 34	35 − 39	40 − 44
No. of persons	4	20	38	24	10	9

Answer 1

Assumed Mean (A) = 32

Age	Mid value (x)	Frequency (f)	d = `(x - "A")/4`	fd
15 − 19	17	4	= `(17 - 32)/4` = −3.75	−15
20 − 24	22	20	= `(22 - 32)/4` = −2.5	−50
25 − 29	27	38	= `(27 - 32)/4` = −1.25	−47.5
30 − 34	32	24	= `(32 - 32)/4` = 0	0
35 − 39	37	10	= `(37 - 32)/4` = 1.25	12.5
40 − 44	42	9	= `(42 - 32)/4` = 2.5	22.5
		`sumf` = 105		`sumf"d"` = −77.5

Arithmetic mean =  `"A" + (sumf"d")/(sumf) xx "c"`

= `32 + ((-77.5)/105 xx 4)`

= 32 – 2.95

= 29.05

Arithmetic mean = 29.05