Question

The coefficient of variation of two distributions are $60$ and $70$. The standard deviation are $21$ and $16$ respectively, then their mean is

• A. $35$
• B. $23$
• C. $28.25$
• D. $22.85$

Answer 1

Answer: (A), (D)

The correct options are
A $35$
D $22.85$

The coefficient of variation $C.V$ with standard deviation $\sigma$ and with arithmetic mean $\stackrel{\_}{x}$ is defined as:

$C.V=\frac{\sigma }{\stackrel{\_}{x}}\times 100$

Let us find the mean $\stackrel{\_}{x}$ of the first distribution with coefficient of variation $C.V=60$ with standard deviation $\sigma =21$:

$60=\frac{21}{\stackrel{\_}{x}}\times 100\Rightarrow 60\stackrel{\_}{x}=2100\Rightarrow \stackrel{\_}{x}=\frac{2100}{60}=35$

Now we find the mean $\stackrel{\_}{y}$ of the first distribution with coefficient of variation $C.V=70$ with standard deviation $\sigma =16$:

$70=\frac{16}{\stackrel{\_}{y}}\times 100\Rightarrow 70\stackrel{\_}{y}=1600\Rightarrow \stackrel{\_}{y}=\frac{1600}{70}=22.85$

Hence, the mean of the given distributions is $35$ and $22.85$.