When 10 observations are taken the random error is x when 100 observations are taken the random error becomes

Since error is measured for 100 observations instead of 10 observations, so error will reduce by $\frac{10}{100}=\frac{1}{10}$ factor
$\therefore \mathrm{Hence} \mathrm{random} \mathrm{error} =\frac{\mathrm{X}}{10}$