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ОПИСАТЕЛЬНАЯ статистика СХЕМА АНАЛИЗ ДАННЫХ 5
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Описательная статистика - схема. Анализ данных #5. Что такое описательная статистик? Какова схема описательного анализа? В теме рассматриваются описательные статистики, шкалы данных, графическое представление, частотная таблица, расчетные статистики. • На первом этапе анализа данных обычно дают общую характеристику собранных сведений. Для этого работают с описательными статистиками, которые различаются в зависимости от типа шкалы. • Для номинальных и порядковых шкал описательными статистиками являются круговые и столбиковые диаграммы, а также частотные таблицы. • Выборочное среднее арифметическое (Mean) самая распространенная описательная статистика, позволяющая быстро охарактеризовать выборку количественных значений. Это ее основной плюс. Минус – это то что среднее не всегда адекватно отражает значения выборки. • Медиана (Median) – это значение в отсортированной выборке, которое делит ее на две равные части, т.е. для ее расчёта необходимо сделать два шага: 1) отсортировать выборку, расположив ее элементы от большего к меньшему; 2) если в выборке 2.1) нечетное число элементов, то найти число, которое делит ее пополам, если 2.2) четное, что от двух серединных значений найти среднее арифметическое. Отсортируем данные в таблице ниже, рассчитаем медианы. • Точка, отделяющая 25% выборки, начиная с минимального значения, называется нижняя квартиль, а точка, отделяющая 75% выборки, начиная с минимального значения, называется верхняя квартиль. Оставшиеся в центре 50% выборки – это квартильный размах. • На базе этих статистик строится ящичная гистограмма (box-plot, ящик с усами), она служит для оценки выборки, с точки зрения квартилей, квартильного размаха, выбросов, грубых ошибок, медианы и распределения данных. • По итогам анализа диаграммы грубые ошибки (экстремальные значения) должны быть исключены из анализа или рассмотрены отдельно. Решение об оставлении или исключении выбросов может быть принято с учетом знания изучаемого явления и целей анализа. • Помимо квартильного размаха рассчитывают и просто размах выборки (Range). Он представляет собой разницу между максимальным и минимальным значениями выборки. • Дисперсия (Variance) – это мера рассеянья переменной. Среднее арифметическое квадратов отклонений переменной от ее среднего значения. • Выборочное стандартное отклонение (Std. Deviation) – еще одна характеристика отклонения от среднего значения. 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