Question

The following table gives the distribution of the life time of 400 neon lamps:

Life time (in hours)	Number of lamps
1500 – 2000	14
2000 – 2500	56
2500 – 3000	60
3000 – 3500	86
3500 – 4000	74
4000 – 4500	62
4500 – 5000	48

Find the average life time of a lamp.

Answer 1

Life time (in hours)	Number of lamps (f)	Mid x	d	fd
1500 – 2000	14	1750	–1500	–21000
2000 – 2500	56	2250	–1000	–56000
2500 – 3000	60	2750	–500	–30000
3000 – 3500	86	3250	0	0
3500 – 4000	74	3750	500	37000
4000 – 4500	62	4250	1000	62000
4500 – 5000	48	4750	1500	72000
	400			64000

Using Assumed Mean Method,

Mean = `"a" + (sum"fd")/(sum"f")`

a = 3250

Mean = `3250 + 64000/400`

= 3250 + 160

= 3410

Average life of lamp is 3410 hr.