Średnia ważona
Średnia ważona\textcolor{#E94D00}{\overline{x_w}} xw liczb\textcolor{#75A600}{x}_{\textcolor{#75A600}{1}}\textcolor{#75A600}{,x}_{\textcolor{#75A600}{2}}\textcolor{#000000}{,}\textcolor{#75A600}{x}_{\textcolor{#75A600}{3}},\textrm{ ...},\textcolor{#75A600}{x}_{\textcolor{#75A600}{k}}, x1, x2, x3, ..., xk, którym przypisano dodatnie wagi – odpowiednio\textcolor{#005FD4}{n}_{\textcolor{#005FD4}{1}},\textcolor{#005FD4}{n}_{\textcolor{#005FD4}{2}},\textcolor{#005FD4}{n}_{\textcolor{#005FD4}{3}},\textrm{ ...},\textcolor{#005FD4}{n}_{\textcolor{#005FD4}{k}} n1, n2, n3, ..., nk – jest równa:
\overline{\textcolor{#E94D00}{x_w}} xw \textcolor{#000000}{=\frac{\textcolor{#75A600}{x}_{\textcolor{#75A600}{1}}\cdot \textcolor{#005FD4}{n}_{\textcolor{#005FD4}{1}}+\textcolor{#75A600}{x}_{\textcolor{#75A600}{2}}\cdot \textcolor{#005FD4}{n}_{\textcolor{#005FD4}{2}}+\textcolor{#75A600}{x}_{\textcolor{#75A600}{3}}\cdot \textcolor{#005FD4}{n}_{\textcolor{#005FD4}{3}}+\textrm{ ... }+\textcolor{#75A600}{x}_{\textcolor{#75A600}{k}}\cdot \textcolor{#005FD4}{n}_{\textcolor{#005FD4}{k}}}{\textcolor{#005FD4}{n}_{\textcolor{#005FD4}{1}}+\textcolor{#005FD4}{n}_{_{}\textcolor{#005FD4}{2}}+\textcolor{#005FD4}{n}_{\textcolor{#005FD4}{3}}+\textrm{ ... }+\textcolor{#005FD4}{n}_{\textcolor{#005FD4}{k}}}} = x1 ⋅ n1 + x2 ⋅ n2 + x3 ⋅ n3 + ... + xk ⋅ nkn1 + n2 + n3 + ... + nk
Przykłady
1. Średnia ważona liczb:\textcolor{#75A600}{7},\textcolor{#75A600}{7},\textcolor{#75A600}{5}\textcolor{#000000}{,} 7, 7, 5, z wagami odpowiednio:\textcolor{#005FD4}{1},\textcolor{#005FD4}{2},\textcolor{#005FD4}{3}, 1, 2, 3, jest równa:
\overline{\textcolor{#E94D00}{x_w}} xw \textcolor{#000000}{=\frac{\textcolor{#75A600}{7}\cdot \textcolor{#005FD4}{1}+\textcolor{#75A600}{7}\cdot \textcolor{#005FD4}{2}+\textcolor{#75A600}{5}\cdot \textcolor{#005FD4}{3}}{\textcolor{#005FD4}{1}+\textcolor{#005FD4}{2}+\textcolor{#005FD4}{3}}=} = 7 ⋅ 1 + 7 ⋅ 2 + 5 ⋅ 31 + 2 + 3 =
=\frac{7+14+15}{6}=6 = 7 + 14 + 156 = 6
2. Średnia ważona ocen Oli zestawionych w tabeli:
