Công thức tính độ lệch chuẩn nếu biết phương sai \(s_X^2\) là:

\(\overline x = \dfrac{{{n_1}{x_1} + {n_2}{x_2} + ... + {n_k}{x_k}}}{{{n^2}}}\)

\(\overline x  = \dfrac{{{n_1}{x_1} + {n_2}{x_2} + ... + {n_k}{x_k}}}{n}\)

\(\overline x  = {n_1}{x_1} + {n_2}{x_2} + ... + {n_k}{x_k}\)

\(\overline x  = n\left( {{n_1}{x_1} + {n_2}{x_2} + ... + {n_k}{x_k}} \right)\)

\(s_X^2 = \dfrac{1}{n}\left[ {{n_1}{{\left( {{x_1} - \overline x } \right)}^2} + {n_2}{{\left( {{x_2} - \overline x } \right)}^2} + ... + {n_k}{{\left( {{x_k} - \overline x } \right)}^2}} \right]\)

\(s_X^2 = \dfrac{1}{n}\left[ {{{\left( {{x_1} - \overline x } \right)}^2} + {{\left( {{x_2} - \overline x } \right)}^2} + ... + {{\left( {{x_k} - \overline x } \right)}^2}} \right]\)

\(s_X^2 = {\left( {{x_1} - \overline x } \right)^2} + {\left( {{x_2} - \overline x } \right)^2} + ... + {\left( {{x_k} - \overline x } \right)^2}\)

\(s_X^2 = \dfrac{1}{{{n^2}}}\left[ {{n_1}{{({x_1} - \overline x )}^2} + {n_2}{{({x_2} - \overline x )}^2} + ... + {n_k}{{({x_k} - \overline x )}^2}} \right]\)