Coefficient of variation of two distributions are 60 and70, and their standard deviations arc 21 and 16, respectively. The sum of their arithmetic means is

Question

Coefficient of variation of two distributions are $$60$$ $$and70$$, and their standard deviations arc $$21$$ and $$16$$, respectively. The sum of their arithmetic means is

Infinity Learn · Accepted Answer

Given C.V. (1st$$ $$distribution) $$=60$$,σ$$1=21$$ C.V. (2nd$$ $$distribution) $$=70$$,σ$$2=16$$ Let $$x1$$¯ and $$x2$$¯ be the means of $$1$$ st and $$2$$ nd distribution,  respectively. Then  C.V. (1st$$ $$distribution) $$=$$σ$$1x$$¯$$1$$×$$100$$ Therefore $$60=21x$$¯$$1$$×$$100$$ or x¯¯$$1=2160$$×$$100=35$$ And C.V. $$2nd$$  $$distribution)$$ $$=$$σ$$2x$$¯$$2$$×$$100$$ i.e., $$70=16x$$¯$$2$$×$$100$$ or $$x2$$¯$$=1670$$×$$100=22.85$$      Sum of means $$=$$ $$35$$ $$+$$ $$22.85$$ $$=57.85$$

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Coefficient of variation of two distributions are 60 and70, and their standard deviations arc 21 and 16, respectively. The sum of their arithmetic means is

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