Question

The weights of 50 apples were recorded as given below. Calculate the mean weight, to the nearest gram. by the Step Deviation Method.

Weights in grams	No. of apples
80 - 55	5
85 - 90	8
90 - 95	10
95 - 100	12
100 - 105	8
105 - 110	4
110 - 115	3

Answer 1

Weight in grams.	No. of apples	`bb(x_i)`	`bb(x_i - "A")`	`bb(u_i = (x_i - "A")/(5))`	`bb(f_iu_i)`
80 - 85	5	82.5	−15	−3	−15
85 - 90	8	87.5	−10	−2	−16
90 - 95	10	92.5	−5	−1	−10
95 - 100	12	(97.5)A	0	0	0
100 - 105	8	102.5	5	1	8
105 - 110	4	107.5	10	2	8
110 - 115	3	112.5	15	3	9
	`sumf_i = 50`				`sumf_iu_i = -16`

A = 97.5, `sumf_i = 50, sumf_iu_i = -16, "h" = 5`.

∴ Mean `bar"X" = "A" + (sumf_iu_i)/(sumf_i) xx "h"`

= 97.5 + `(-16)/(50) xx 5`

= 95·9.

= 96 g