Решебник по математике 8 класс. вероятность и статистика Высоцкий ФГОС Часть 1 Задание 317

\[\boxed{\mathbf{317.}}\]

\[\overline{x_{д}} = 166,3;\ \ \ S_{д}^{2} = 8,5;\]

\[\overline{x_{д}} = \frac{x_{1} + x_{2} + x_{3} + \ldots + x_{n}}{n} =\]

\[= 166,3\]

\[x_{1} + x_{2} + x_{3} + \ldots + x_{n} = 166,3n.\]

\[\overline{x_{м}} = 177,6;\ \ S_{м}^{2} = 9,6;\]

\[\overline{x_{м}} = \frac{y_{1} + y_{2} + y_{3} + \ldots + y_{n}}{n} =\]

\[= 177,6.\]

\[y_{1} + y_{2} + y_{3} + \ldots + y_{n} = 177,6n.\]

\[\overline{x} = \frac{166,3n + 177,6n}{2n} =\]

\[= 171,95 \approx 172\ (см) - средний\ \]

\[рост.\]

\[S_{д}^{2} = \overline{x^{2}} - {166,3}^{2} = 8,5\]

\[\overline{x^{2}} = 27664,19.\]

\[S_{м}^{2} = \overline{y^{2}} - {177,6}^{2} = 9,6\]

\[\overline{y^{2}} = 31551,36.\]

\[\frac{27664,19 + 31551,36}{2} =\]

\[= 29607,775.\]

\[S = 29607,775 - (172)^{2} \approx\]

\[\approx 23,78\ см^{2}.\]

\[Ответ:172\ см;\ 23,78\ см^{2}.\]