Question

C.V of 2 series is given as 48% and 60% and standard deviation is given as 24 and
15 respectively. Find Arithmetic Mean.​

Answer 1

Answer:

CV1 = (σ1/A1)100. i.e., 0.6 = (45/A1)100 so that A1 = 7500

CV2= (σ2/A2)100. i.e., 0.75 = (40/A2)100 so that A2 = 16000/3

A1:A2 = 7500:(16000/3) = 22500:16000 = 45:32

Hence the ratio of arithmetic means = 45:32

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Answer 2

Given are the C.Vs and standard deviations of two data sets, find their Arithmetic means.

Explanation:

• Coefficient of Variation is the standard measure of the dispersion of a probability or frequency distribution.
• It is also referred to as the relative standard deviation and is mathematically defined as the ratio of the standard deviation and the mean of the distribution.
• The C.V of a distribution having standard deviation $\sigma$ and mean $\mu$ is given by $C.V=(\frac{\sigma}{\mu}x100)\%$  
• Hence from the given question we get required means as, $CV_1=48\%\ \ \sigma_1=24,\ \ \ CV_2=60\%\ \ \sigma_2= 15\\->48\%=\frac{24}{\mu_1}(100)\ \ \ \ ->60\%=\frac{15}{\mu_2}(100)\\->\mu_1=50 \ \ \ \ \ \ \ \ \ \ \ \ \ ->\mu_2=25$
• The arithmetic means are $50\ and\ 25$.