Mathematics · important
Combined variance of two groups for JEE
Calculation of standard deviation, variance and mean deviation for grouped and ungrouped data
Formula
\(\sigma^2=\frac{n_1\left(\sigma_1^2+(\bar{x}_1-\bar{x})^2\right)+n_2\left(\sigma_2^2+(\bar{x}_2-\bar{x})^2\right)}{n_1+n_2}\)
Variables: \(n_1,n_2\): sizes, \(\bar{x}_1,\bar{x}_2\): means, \(\sigma_1,\sigma_2\): standard deviations, \(\bar{x}\): combined mean.
Conditions: For combining two data sets.
Mixture/merged data problems.