Question

Life of bulbs produced by two factories A and B are given below:

Length of life (in hours)	Factory A (Number of bulbs)	Factory B (Number of bulbs)
550 – 650	10	8
650 – 750	22	60
750 – 850	52	24
850 – 950	20	16
950 – 1050	16	12
	120	120

The bulbs of which factory are more consistent from the point of view of length of life?

Answer 1

Here h = 100

Let A (assumed mean) = 800.

Length of life (in hour)	Mid values `(x_i)`	`y_i = (x_i - A)/10`	Factory A			Factory B
			`f_i`	`f_iy_i`	`f_iy_i^2`	`f_i`	`f_iy_i`	`f_iy_i^2`
550 – 650	600	–2	10	–20	40	8	–16	32
650 – 750	700	–1	22	–22	22	60	– 60	60
750 – 850	800	0	52	0	0	24	0	0
850 – 950	900	1	20	20	20	16	16	16
950 – 1050	1000	2	16	32	64	12	24	48
			120	10	146	120	–36	156

For factory A

Mean `(barx) = 800 + 10/120 xx 100` = 816.67 hours

S.D. = `100/120 sqrt(120(146) - 100)` = 109.98 

Therefore, Coefficient of variation (C.V.) = `(S.D.)/barx xx 100`

= `109.98/816.67 xx 100`

= 13.47

For factory B

Mean = `800 + (-36)/120 100` = 770

S.D. = `100/120 sqrt(120(156) - (-36)^2)` = 110

Therefore, Coefficient of variation = `(S.D.)/"Mean" xx 100`

= `110/770 xx 100`

= 14.29

Since C.V. of factory B > C.V. of factory A

⇒ Factory B has more variability which means bulbs of factory A are more consistent.