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NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Mathematics
Chapter: Statistics

NTA Abhyas 2020 · Mathematics · Statistics

Coefficient of variation of two distributions are 60% and 75%, and...

Coefficient of variation of two distributions are

60%

and

75%,

and their standard deviation are

18

and

15

respectively, then their arithmetic means respectively are

Options

A $30, 30$
B $30, 20$
C $20, 30$
D $20, 20$

Correct answer

B. $30, 20$

Step-by-step solution

Given,

C{V}_{1} = 60, {CV}_{2} = 75, {\sigma}_{1} = 18

and

{\sigma}_{2} = 15

Let

{\overset{-}{x}}_{1}

and

{\overset{-}{x}}_{2}

be the means of

{1}^{st}

and

{2}^{nd}

distribution respectively.
Then,

C{V}_{1} = \dfrac{{\sigma}_{1}}{{\overset{-}{x}}_{1}} \times 100 ⇒ {\overset{-}{x}}_{1} = \dfrac{18 \times 100}{60} = 30

C{V}_{2} = \dfrac{{\sigma}_{2}}{{\overset{-}{x}}_{2}} \times 100 ⇒ {\overset{-}{x}}_{2} = \dfrac{15 \times 100}{75} = 20

Hence,

{\overset{-}{x}}_{1} = 30

and

{\overset{-}{x}}_{2} = 20

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