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Q.
The coefficient of variation of the first $5$ prime numbers is
TS EAMCET 2020
Solution:
First prime number is $2,3,5,7,11$
$\bar{x}=\frac{2+3+5+7+11}{5}=\frac{28}{5}$
$\Sigma x_{i}^{2}=4+9+25+49+121=208$
$\sigma=\sqrt{\frac{\Sigma x_{i}^{2}}{5}-(\bar{x})^{2}}$
$\sigma=\sqrt{\frac{208}{5}-\left(\frac{28}{5}\right)^{2}}$
$=\sqrt{\frac{1040-784}{25}}=\frac{16}{5}$
$C . V=\frac{\sigma}{x} \times 100$
$=\frac{16}{28} \times 100=\frac{400}{7}$