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 gives higher life?

Answer 1

For Brand A 

Life (in hrs)	No. of bulbs	M	A = 125	d = `(x - A)/i`	`d^{'2}`	fd'	`fd^{'2}`
0 - 50	f	x	X - A = d
	15	25	-	-2	4	-30	60
			100
50 - 100	20	75	-	-1	1	-20	20
			50
100 - 150	18	125	0	0	0	0	0
150 - 200	25	175	50	1	1	25	25
200 - 250	22	225	100	2	4	44	88
	∑f = 100					`sumfd^' = 19`	`sumfd^{'2} = 193`

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

= `125 + 19/100 xx 50`

= 134.5

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

= `sqrt(193/100 - (19/100)^2 xx 50)`

= `sqrt(193/100 - 361/10000) xx 50`

= `sqrt(18939/10000) xx 50`

= 68.5

CV = `sigma/overlineX xx 100`

= `68.5/134.5 xx 100`

= 50.93

The average life of the bulb of Brand B has a comparatively higher life than the bulb of Brand A.