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Statistics Solution for this Question

	Factory A	Factory B
Number of Employees	–	–
Average Wages (₹) (𝜇)	1200	100
Variance (σ²)	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 = (σ / μ) × 100

Factory A:

μ_A = 1200
σ²_A = 81 → σ_A = √81 = 9

Cv(A) = (9 / 1200) × 100 = 0.75%

Factory B:

μ_B = 100
σ²_B = 256 → σ_B = √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%).

(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:

σnew² = σ² + [(xtrue - μ)² - (xwrong - μ)²] / n

x_true = 910
x_wrong = 900
μ = 100
σ² = 256
n = 100

σnew² = 256 + [(910 - 100)² - (900 - 100)²] / 100
= 256 + (656100 - 640000) / 100
= 256 + 16100 / 100
= 256 + 161
= 417

✅ Conclusion (b):
Corrected Variance (σ²) = 417

Note:
- μ = Mean
- σ² = Variance
- σ = Standard Deviation
- C_v = Coefficient of Variation

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