Statistics Solution for this Question
| Factory A | Factory B | |
|---|---|---|
| Number of Employees | – | – |
| Average Wages (₹) (ЁЭЬЗ) | 1200 | 100 |
| Variance (╧Г²) | 81 | 256 |
(a) In which factory is there greater variation in the distribution of wages per employee?
We calculate the Coefficient of Variation (C.V.) using:
Cv = (╧Г / ╬╝) × 100
Factory A:
╬╝A = 1200
╧Г²A = 81 → ╧ГA = √81 = 9
Cv(A) = (9 / 1200) × 100 = 0.75%
Factory B:
╬╝B = 100
╧Г²B = 256 → ╧ГB = √256 = 16
Cv(B) = (16 / 100) × 100 = 16%
✅ Conclusion (a):
Factory B has a greater variation in wages because its C.V. (16%) is greater than Factory A (0.75%).
Factory B has a greater variation in wages because its C.V. (16%) is greater than Factory A (0.75%).
(b) Suppose in factory B, the wages of an employee were wrongly noted as ₹900 instead of ₹910.
To correct the variance, use the formula:
╧Гnew² = ╧Г² + [(xtrue - ╬╝)² - (xwrong - ╬╝)²] / n
xtrue = 910
xwrong = 900
╬╝ = 100
╧Г² = 256
n = 100
╧Гnew² = 256 + [(910 - 100)² - (900 - 100)²] / 100
= 256 + (656100 - 640000) / 100
= 256 + 16100 / 100
= 256 + 161
= 417
✅ Conclusion (b):
Corrected Variance (╧Г²) = 417
Corrected Variance (╧Г²) = 417
Note:
- ╬╝ = Mean
- ╧Г² = Variance
- ╧Г = Standard Deviation
- Cv = Coefficient of Variation
- ╬╝ = Mean
- ╧Г² = Variance
- ╧Г = Standard Deviation
- Cv = Coefficient of Variation
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