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प्रश्न
If the mean of the weight of packet is 12.9 gm. Find the value of b.
| Weight of packet | 0 – 5 | 5 – 10 | 10 – 15 | 15 – 20 | 20 – 25 |
| Number of packets | 3 | b | 8 | 5 | 4 |
योग
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उत्तर
1. Construct the frequency table
| Weight of packet (Class Interval) |
Number of packets (fi) |
Class Midpoint (xi) |
fi × xi |
| 0 – 5 | 3 | 2.5 | 3 × 2.5 = 7.5 |
| 5 – 10 | b | 7.5 | 7.5b |
| 10 – 15 | 8 | 12.5 | 8 × 12.5 = 100 |
| 15 – 20 | 5 | 17.5 | 5 × 17.5 = 87.5 |
| 20 – 25 | 4 | 22.5 | 4 × 22.5 = 90 |
| Total | Σfi = 20 + b | Σfixi = 285 + 7.5b |
2. Substitute into the mean formula
Given that the Mean `(barx) = 12.9`:
`12.9 = (285 + 7.5b)/(20 + b)`
Cross-multiply to solve for b:
12.9 × (20 + b) = 285 + 7.5b
258 + 12.9b = 285 + 7.5b
Rearrange the terms by moving b terms to one side and constants to the other side:
12.9b – 7.5b = 285 – 258
5.4b = 27
`b = 27/5.4`
b = 5
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