Question

A company has two departments with 42 and 60 employees respectively. Their average weekly wages are Rs. 750 and Rs. 400. The standard deviations are 8 and 10 respectively. Which department has a larger bill?

Answer 1

Let n₁ = 42, n₂ = 60, ${\displaystyle \overline{{\text{x}}_1}}$ = 750, ${\displaystyle \overline{{\text{x}}_2}}$ = 400, σ₁ = 8, σ₂ = 10

C.V. (1) = ${\displaystyle 100\times \frac{{\sigma }_1}{\overline{{\text{x}}_1}}=100\times \frac{8}{750}}$ = 1.07%

C.V. (2) = ${\displaystyle 100\times \frac{{\sigma }_2}{\overline{{\text{x}}_2}}=100\times \frac{10}{400}}$ = 2.5%

Since, ${\displaystyle \overline{{\text{x}}_1}>\overline{{\text{x}}_2}}$
i.e., average weekly wages are more for first department.
∴ first department has a larger bill.