Question

Find the mean, variance and standard deviation using short-cut method.

Height in cms	70 - 75	75 - 80	80 - 85	85 - 90	90 - 95	95 - 100	100 - 105	105 - 110	110 - 115
No. of children	3	4	7	7	15	9	6	6	3

Answer 1

Class Interval	Mid-point	Frequency	yi	fiyi	yi2	fi2
70 - 75	72.5	3	−4	−12	16	48
75 - 80	77.5	4	−3	−12	9	36
80 - 85	82.5	7	−2	−14	4	28
85 - 90	87.5	7	−1	7	1	7
90 - 50	92.5	15	0	0	0	0
95 - 100	97.5	9	1	9	1	9
100 - 105	102.5	6	2	12	4	24
105 - 110	107.5	6	3	18	9	54
110 - 115	112.5	3	4	12	16	48
Sum	-	60	-	6	-	254

Mean, `overlinex = A + ((sumf_iy_i))/N xx h`

= `9.25 + 6/60 xx 5`

= 92.5 + 0.5 

= 93

Variance, σ² = `h^2/N^2[Nsum f_iy_i^2 - (sumf_iy_i)^2]`

= `25/3600 [60 xx 254 - 36]`

= `12/144 [5 xx 254 - 3]`

= `1/12 [1270 - 3]`

= `1267/12`

= 105.58

Standard deviation, σ = `sqrt(105.58)`

= 10.28