Coefficient of variation of the two distributions are 60% and 80% respectively, and their standard deviations are 21 and 16 respectively.

Question:

Coefficient of variation of the two distributions are 60% and 80% respectively, and their standard deviations are 21 and 16 respectively. Find their arithmetic means

 

Solution:

Given: Coefficient of variation of two distributions are 60% and 80% respectively, and their standard deviations are 21 and 16 respectively.

Need to find: Arithmetic means of the distributions.

For the first distribution,

Coefficient of variation (CV) is $60 \%$, and the standard deviation (SD) is 21 .

We know that,

$\Rightarrow \mathrm{CV}=\frac{\mathrm{SD}}{\text { Mean }} \times 100$

$\Rightarrow \quad$ Mean $=\frac{\mathrm{SD}}{\mathrm{CV}} \times 100$

$\Rightarrow$ Mean $=\frac{21}{60} \times 100$

$\Rightarrow$ Mean $=35$

For the first distribution,

Coefficient of variation (CV) is $80 \%$, and the standard deviation (SD) is 16 .

We know that,

$\Rightarrow \mathrm{CV}=\frac{\mathrm{SD}}{\text { Mean }} \times 100$

$\Rightarrow \quad$ Mean $=\frac{\mathrm{SD}}{\mathrm{CV}} \times 100$

$\Rightarrow \quad$ Mean $=\frac{16}{80} \times 100$

$\Rightarrow$ Mean $=20$

Therefore, the arithmetic mean of $1^{\text {st }}$ distribution is 35 and the arithmetic mean of $2^{\text {nd }}$ distribution is 20 .

 

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