First slide

Introduction to statistics

Question

Coefficients of variation of two distributions are 50 and 60, and their arithmetic means are 30 and 25, respectively. Difference of their standard deviations is

Moderate

A

0
B

1
C

1.5
D

2.5

Solution

$\begin{array}{l} Here, (C V)_{1} = 50, (C V)_{2} = 60, {\bar{x}}_{1} = 30 and {\bar{x}}_{2} = 25 \\ ∴ (C V)_{1} = \frac{σ_{1}}{\bar{x_{1}}} \times 100 \\ \Rightarrow 50 = \frac{σ_{1}}{30} \times 100 \\ ∴ σ_{1} = \frac{30 \times 50}{100} = 15 \\ and C V_{2} = \frac{σ_{2}}{\bar{x_{2}}} \times 100 \\ \Rightarrow 60 = \frac{σ_{2}}{25} \times 100 \\ ∴ σ_{2} = \frac{60 \times 25}{100} = 15 \\ Now, σ_{1} - σ_{2} = 15 - 15 = 0 \end{array}$

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