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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.
Solution
| 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.
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