If 2 data sets having 10 and 20 observations have coefficients of...

Given,

${n}_{1} = 10, \overset{¯}{x}1 = 30, C{V}_{1} = 50$
${n}_{2} = 20, \overset{¯}{x}1 = 25, C{V}_{2} = 60$
$C{V}_{1} = \dfrac{{\sigma}_{1}}{{\overset{¯}{x}}_{1}} \times 100 ⇒ 50 = \dfrac{{\sigma}_{1}}{30} \times 100 ⇒ {\sigma}_{1} = 15$
$C{V}_{2} = \dfrac{{\sigma}_{2}}{{\overset{¯}{x}}_{2}} \times 100 ⇒ 60 = \dfrac{{\sigma}_{1}}{25} \times 100 ⇒ {\sigma}_{2} = 15$
Combined mean $= \dfrac{10 \times 30 + 20 \times 25}{30} = \dfrac{80}{3}$
${d}_{1} = \overset{¯}{x}1 - \overset{¯}{x} = \dfrac{10}{3}, {d}_{2} = \overset{¯}{x} - \overset{¯}{x}2 = \dfrac{5}{3}$
Combined variance $= \dfrac{{n}_{1}{σ}_{1}^{2} + {n}_{2}{σ}_{2}^{2} + {n}_{1}{d}_{1}^{2} + {n}_{2}{d}_{2}^{2}}{{n}_{1} + {n}_{2}}$
$= \dfrac{2250 + 4500 + \dfrac{1000}{9} + \dfrac{500}{9}}{30}$
$= \dfrac{6225}{27} = \dfrac{2075}{9}$