Question

The coefficient of variation of the first $5$ prime numbers is

• A. $\frac{400}{7}$
• B. $\frac{406}{7}$
• C. $\frac{416}{7}$
• D. $\frac{425}{8}$

Answer 1

Answer: (A)

First prime number is $2,3,5,7,11$
$\bar{x}=\frac{2+3+5+7+11}{5}=\frac{28}{5}$
$\Sigma x_i^2=4+9+25+49+121=208$
$\sigma =\sqrt{\frac{\Sigma x_i^2}{5}-(\bar{x}{)}^2}$
$\sigma =\sqrt{\frac{208}{5}-{\left(\frac{28}{5}\right)}^2}$
$=\sqrt{\frac{1040-784}{25}}=\frac{16}{5}$
$C.V=\frac{\sigma }{x}\times 100$
$=\frac{16}{28}\times 100=\frac{400}{7}$