Question

To check the quality of two brands of lightbulbs, their life in burning hours was estimated as under for 100 bulbs of each brand.

Life (in hrs)	No. of bulbs
	Brand A	Brand B
0 - 50	15	2
50 - 100	20	8
100 - 150	18	60
150 - 200	25	25
200 - 250	22	5
	100	100

Which brand is more dependable?

Answer 1

For Brand B

Life (in hrs)	No. of bulbs (f)	Mid value M	A = 125	d' = `(X - A)/c`	`d^{'2}`	fd'	`fd^{'2}`
0 - 50	2	25	-	-2	4	-4	8
			100
50 - 100	8	75	-	-1	1	-8	8
			50
100 - 150	60	125	0	0	0	0	0
150 - 200	25	175	50	1	1	25	25
200 - 250	5	225	100	2	4	10	20
	∑f = 100					`sumfd^' = 23`	`sumfd^{'2} = 61`

`overlineX = A + (sumfd^')/(sumf) xx i`

= `125 + 23/100 xx 50`

= 136.5

`sigma = sqrt((sumfd^{'2})/(sumf) - ((sumfd^')/(sumf))^2 xx i)`

= `sqrt(61/100 - (23/100)^2 xx 50)`

= `sqrt(61/100 - 529/10000) xx 50`

= `sqrt(5571/10000) xx 50`

= 37.5

CV = `sigma/overlineX xx 100`

= `37.5/136.5 xx 100`

= 27.47

The bulbs of Brand B are more dependable as the CV of Brand B is lesser than the CV of Brand A.