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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.

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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,

For the first distribution, 

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

We know that,

CV = \(\frac{SD}{Mean}\times100\) 

Mean =   \(\frac{SD}{CV}\times100\) 

 Mean =   \(\frac{21}{60}\times100\) 

Mean = 35

For the first distribution, 

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

We know that,

CV = \(\frac{SD}{Mean}\times100\) 

Mean =   \(\frac{SD}{CV}\times100\) 

 Mean =   \(\frac{16}{80}\times100\) 

Mean = 20

Therefore, the arithmetic mean of 1st distribution is 35 and the arithmetic mean of 2nd distribution is 20.

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