1.

Co-efficient of variation of two distributions are 50 and 60 and their arithmetic means are 30 and 25 respectively. Find the difference of their standard deviation.

Answer»

Given,

C.V1= 50, 

C.V2 = 60

\(\bar{x_1}=30\),

\(\bar{x_2}=25\) 

We Know:

C.V = \(\frac{σ}{x}\times100\) 

⇒ \(\bar{x}=\)\(\frac{σ}{C.V}\times100\) 

∴ \(\bar{x_1}=\)\(\frac{σ_1}{C.V_1}\times100\) 

⇒ 30 = \(\frac{σ_1}{50}\times100\) 

⇒ \(σ_1\) = 15 

And,

\(\bar{x_2}=\) \(\frac{σ_2}{C.V_2}\times100\) 

⇒ 25 = \(\frac{σ_2}{60}\times100\) 

⇒ \(σ_2\) \(=25\frac{3}{5}\)

⇒ \(σ_2\) \(=15\)

∴ Required difference

= \(σ_1-σ_2\) 

= 15 − 15

= 0


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