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Построение вариационного ряда
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Работа выполняется группой студентов (2-3 человека).
Выпишите числовые показатели в порядке убывания или нарастания величин.
Вариант 1. Высота ольхи (м).
| 10, 4 | 14, 4 | 11, 5 | 11, 4 | 14, 1 | 14, 3 | 12, 6 | 10, 9 | ||
| 9, 2 | 14, 5 | 10, 8 | 11, 2 | 11, 5 | 12, 5 | 12, 7 | 11, 3 | ||
| 10, 1 | 9, 4 | 10, 6 | 12, 4 | 11, 3 | 9, 3 | 11, 6 | 12, 4 | ||
| 11, 4 | 9, 6 | 10, 5 | 11, 7 | 10, 3 | 11, 7 | 11, 2 | 14, 6 | 12, 3 | |
| 14, 7 | 11, 5 | 9, 8 | 14, 8 | 14, 9 | 10, 5 | 11, 8 | 14, 1 | 14, 2 | |
| 14, 3 | 12, 3 | 15, 1 | 12, 2 | 15, 2 | 11, 6 | 13, 8 | 15, 3 | 12, 1 | |
| 15, 5 | 13, 7 | 12, 8 | 13, 6 | 12, 7 | 13, 5 | 11, 7 | 13, 4 | ||
| 12, 6 | 13, 9 | 12, 5 | 15, 7 | 12, 9 | 13, 1 | 13, 2 | |||
| 13, 3 | 12, 6 | 13, 8 | 12, 7 | 13, 7 | 12, 8 | 15, 8 | 12, 9 | 13, 6 | |
| 13, 5 | 12, 1 | 12, 2 | 13, 2 | 12, 3 | 13, 3 | 12, 4 | 13, 4 | 12, 5 |
Вариант 2. Длина междоузлий томата (см).
| 12, 1 | 15, 2 | 17, 1 | 15, 2 | 15, 9 | 16, 7 | 14, 5 | 15, 9 | 15, 1 | |
| 14, 4 | 13, 2 | 16, 1 | 16, 5 | 16, 3 | 13, 7 | 15, 1 | 17, 2 | 15, 3 | |
| 15, 3 | 14, 4 | 16, 6 | 14, 6 | 14, 3 | 13, 1 | 14, 5 | 16, 4 | 13, 3 | |
| 16, 2 | 13, 8 | 16, 4 | 15, 2 | 17, 3 | 15, 1 | 12, 3 | 14, 3 | 15, 4 | 16, 8 |
| 15, 8 | 15, 8 | 16, 9 | 12, 9 | 14, 7 | 16, 3 | 14, 6 | 13, 9 | 13, 4 | 16, 5 |
| 16, 6 | 15, 3 | 17, 4 | 14, 2 | 15, 4 | 17, 5 | 17, 8 | 12, 4 | 15, 7 | 15, 5 |
| 12, 6 | 14, 2 | 13, 5 | 14, 8 | 14, 7 | 16, 7 | 13, 5 | |||
| 14, 1 | 15, 4 | 15, 5 | 17, 6 | 15, 5 | 15, 6 | 17, 7 | 12, 5 | 14, 1 | 15, 6 |
| 15, 7 | 16, 2 | 17, 9 | 14, 9 | 16, 9 | 16, 1 | 14, 8 | 16, 8 | ||
| 13, 6 | 18, 1 | 18, 3 | 18, 4 | 18, 7 | 17, 1 | 18, 8 | 17, 2 | 17, 3 |
Вариант 3. Масса тела некоторых пород индюков (кг).
| 15, 1 | 17, 9 | 18, 1 | 19, 3 | 21, 1 | 20, 1 | 20, 7 | 18, 5 | 16, 8 | 17, 8 |
| 15, 2 | 18, 2 | 19, 4 | 21, 3 | 20, 2 | 20, 8 | 18, 6 | 16, 9 | 19, 4 | |
| 18, 4 | 16, 7 | 17, 7 | 19, 2 | 15, 3 | 17, 1 | 18, 3 | 19, 5 | 21, 5 | 20, 3 |
| 19, 8 | 18, 7 | 19, 5 | 16, 6 | 18, 3 | 19, 1 | 17, 6 | 20, 3 | ||
| 17, 2 | 18, 4 | 19, 6 | 20, 4 | 18, 8 | 16, 1 | 19, 6 | 20, 5 | 18, 2 | |
| 18, 5 | 20, 4 | 17, 5 | 20, 2 | 15, 5 | 17, 3 | 18, 5 | 18, 9 | 16, 2 | 19, 7 |
| 19, 7 | 20, 6 | 18, 1 | 16, 3 | 18, 4 | 20, 1 | 21, 8 | 17, 4 | 15, 6 | |
| 16, 3 | 17, 4 | 18, 6 | 19, 8 | 19, 9 | 16, 3 | 18, 3 | |||
| 18, 1 | 17, 3 | 17, 1 | 15, 9 | 17, 5 | 18, 7 | 16, 2 | 17, 7 | 18, 9 | 19, 1 |
| 20, 9 | 18, 2 | 21, 7 | 17, 2 | 16, 1 | 17, 6 | 18, 8 | 19, 2 | 19, 3 |
Вариант 4. Масса тела некоторых пород свиней (ц).
| 3, 5 | 2, 0 | 3, 5 | 3, 3 | 3, 6 | 3, 6 | 4, 1 | 3, 7 | 4, 1 | 3, 5 |
| 3, 0 | 4, 1 | 2, 3 | 4, 1 | 3, 4 | 4, 5 | 3, 5 | 4, 5 | 3, 8 | 5, 0 |
| 3, 6 | 2, 6 | 3, 6 | 2, 2 | 3, 5 | 3, 0 | 4, 2 | 3, 3 | 4, 2 | 3, 9 |
| 3, 1 | 4, 2 | 2, 7 | 4, 2 | 2, 1 | 4, 6 | 3, 1 | 4, 6 | 3, 2 | 5, 1 |
| 3, 7 | 3, 2 | 3, 7 | 2, 9 | 3, 7 | 2, 4 | 4, 3 | 3, 2 | 4, 3 | 3, 1 |
| 3, 6 | 4, 3 | 3, 3 | 4, 3 | 2, 8 | 4, 7 | 2, 5 | 4, 7 | 3, 3 | 5, 3 |
| 3, 8 | 3, 7 | 3, 8 | 3, 4 | 3, 8 | 2, 7 | 4, 4 | 2, 6 | 4, 4 | 3, 4 |
| 3, 8 | 4, 4 | 3, 8 | 4, 4 | 3, 0 | 4, 8 | 2, 6 | 4, 8 | 2, 7 | 5, 4 |
| 3, 9 | 3, 7 | 3, 9 | 3, 9 | 4, 0 | 3, 1 | 4, 0 | 2, 5 | 4, 0 | 2, 8 |
| 3, 9 | 4, 0 | 3, 6 | 4, 3 | 3, 5 | 4, 9 | 3, 2 | 4, 9 | 2, 9 | 5, 1 |
Вариант 5. Масса тела некоторых пород кур (кг).
| 3, 5 | 3, 3 | 4, 1 | 3, 7 | 4, 1 | 3, 5 | 2, 5 | 2, 0 | 3, 6 | 3, 6 |
| 2, 3 | 4, 1 | 3, 5 | 4, 5 | 3, 8 | 5, 0 | 3, 0 | 4, 1 | 3, 4 | 4, 5 |
| 3, 6 | 2, 2 | 4, 2 | 3, 3 | 2, 7 | 3, 9 | 3, 6 | 2, 6 | 3, 5 | 3, 0 |
| 2, 7 | 4, 2 | 3, 1 | 4, 6 | 3, 2 | 2, 0 | 3, 1 | 4, 2 | 2, 1 | 4, 6 |
| 3, 7 | 2, 9 | 2, 8 | 3, 2 | 4, 3 | 3, 1 | 3, 4 | 3, 2 | 3, 7 | 2, 4 |
| 3, 3 | 4, 3 | 2, 5 | 4, 7 | 3, 3 | 5, 3 | 3, 6 | 4, 3 | 2, 8 | 4, 7 |
| 3, 8 | 3, 4 | 4, 4 | 2, 6 | 2, 9 | 3, 4 | 3, 8 | 3, 7 | 3, 8 | 2, 7 |
| 3, 8 | 4, 4 | 2, 6 | 4, 8 | 2, 7 | 5, 4 | 3, 0 | 4, 4 | 3, 0 | 4, 8 |
| 3, 9 | 3, 9 | 4, 0 | 2, 5 | 4, 0 | 2, 8 | 3, 9 | 3, 7 | 4, 0 | 3, 1 |
| 3, 6 | 4, 3 | 3, 2 | 4, 9 | 2, 9 | 5, 1 | 3, 9 | 4, 0 | 3, 5 | 4, 9 |
Вариант 6. Длина початков кукурузы (см).
| 10, 4 | 11, 5 | 14, 3 | 10, 9 | 14, 4 | 11, 4 | 14, 1 | 12, 6 | ||
| 14, 5 | 11, 5 | 11, 3 | 9, 2 | 10, 8 | 11, 2 | 12, 5 | 12, 7 | ||
| 9, 4 | 12, 4 | 9, 3 | 10, 1 | 10, 6 | 11, 3 | 11, 6 | 12, 4 | ||
| 9, 6 | 10, 3 | 11, 2 | 12, 3 | 11, 4 | 10, 5 | 11, 7 | 11, 7 | 14, 6 | |
| 11, 5 | 14, 8 | 10, 5 | 14, 2 | 14, 7 | 9, 8 | 14, 9 | 11, 8 | 14, 1 | |
| 12, 3 | 12, 2 | 11, 6 | 12, 1 | 14, 3 | 15, 1 | 15, 2 | 13, 8 | 15, 3 | |
| 13, 7 | 13, 6 | 13, 5 | 13, 4 | 15, 5 | 12, 8 | 12, 7 | 11, 7 | ||
| 13, 9 | 12, 9 | 12, 6 | 12, 5 | 15, 7 | 13, 1 | 13, 2 | |||
| 12, 6 | 12, 7 | 12, 8 | 12, 9 | 13, 3 | 13, 8 | 13, 7 | 15, 8 | 13, 6 | |
| 12, 1 | 12, 2 | 12, 3 | 12, 4 | 12, 5 | 13, 5 | 13, 2 | 13, 3 | 13, 4 |
Вариант 7. Высота осины (м).
| 16, 7 | 14, 5 | 15, 9 | 15, 2 | 15, 9 | 12, 1 | 15, 2 | 17, 1 | 15, 1 | |
| 13, 7 | 15, 1 | 17, 2 | 16, 5 | 16, 3 | 14, 4 | 13, 2 | 16, 1 | 15, 3 | |
| 14, 3 | 13, 1 | 14, 5 | 16, 6 | 14, 6 | 15, 3 | 14, 4 | 16, 4 | 13, 3 | |
| 15, 1 | 12, 3 | 14, 3 | 15, 2 | 17, 3 | 16, 2 | 13, 8 | 16, 4 | 15, 4 | 16, 8 |
| 16, 3 | 14, 6 | 13, 9 | 12, 9 | 14, 7 | 15, 8 | 15, 8 | 16, 9 | 13, 4 | 16, 5 |
| 17, 5 | 17, 8 | 12, 4 | 14, 2 | 15, 4 | 16, 6 | 15, 3 | 17, 4 | 15, 7 | 15, 5 |
| 14, 7 | 14, 8 | 12, 6 | 14, 2 | 13, 5 | 16, 7 | 13, 5 | |||
| 15, 6 | 17, 7 | 12, 5 | 17, 6 | 15, 5 | 14, 1 | 15, 4 | 15, 5 | 14, 1 | 15, 6 |
| 16, 9 | 16, 1 | 14, 9 | 15, 7 | 16, 2 | 17, 9 | 14, 8 | 16, 8 | ||
| 18, 7 | 17, 1 | 18, 8 | 18, 3 | 18, 4 | 13, 6 | 18, 1 | 17, 2 | 17, 3 |
Вариант 8. Длина листовой пластинки вейника наземного (см).
| 17, 8 | 18, 5 | 20, 1 | 19, 3 | 17, 9 | 15, 1 | 18, 1 | 21, 1 | 20, 7 | 16, 8 |
| 19, 4 | 18, 6 | 20, 2 | 19, 4 | 15, 2 | 18, 2 | 21, 3 | 20, 8 | 16, 9 | |
| 20, 3 | 19, 5 | 17, 1 | 19, 2 | 16, 7 | 18, 4 | 17, 7 | 15, 3 | 18, 3 | 21, 5 |
| 17, 6 | 18, 3 | 19, 5 | 18, 7 | 19, 8 | 16, 6 | 19, 1 | 20, 3 | ||
| 20, 5 | 16, 1 | 20, 4 | 18, 4 | 17, 2 | 19, 6 | 18, 8 | 19, 6 | 18, 2 | |
| 19, 7 | 18, 9 | 17, 3 | 20, 2 | 20, 4 | 18, 5 | 17, 5 | 15, 5 | 18, 5 | 16, 2 |
| 15, 6 | 17, 4 | 20, 1 | 16, 3 | 20, 6 | 19, 7 | 18, 1 | 18, 4 | 21, 8 | |
| 18, 3 | 16, 3 | 19, 8 | 17, 4 | 16, 3 | 18, 6 | 19, 9 | |||
| 19, 1 | 17, 7 | 18, 7 | 15, 9 | 17, 3 | 18, 1 | 17, 1 | 17, 5 | 16, 2 | 18, 9 |
| 19, 3 | 18, 8 | 16, 1 | 17, 2 | 18, 2 | 20, 9 | 21, 7 | 17, 6 | 19, 2 |
Вариант 9. Длина плодов груши (см).
| 3, 0 | 4, 1 | 2, 3 | 4, 1 | 3, 4 | 4, 5 | 3, 5 | 4, 5 | 3, 8 | 5, 0 |
| 3, 1 | 4, 2 | 2, 7 | 4, 2 | 2, 1 | 4, 6 | 3, 1 | 4, 6 | 3, 2 | 5, 1 |
| 3, 6 | 4, 3 | 3, 3 | 4, 3 | 2, 8 | 4, 7 | 2, 5 | 4, 7 | 3, 3 | 5, 3 |
| 3, 8 | 4, 4 | 3, 8 | 4, 4 | 3, 0 | 4, 8 | 2, 6 | 4, 8 | 2, 7 | 5, 4 |
| 3, 9 | 4, 0 | 3, 6 | 4, 3 | 3, 5 | 4, 9 | 3, 2 | 4, 9 | 2, 9 | 5, 1 |
| 3, 8 | 3, 7 | 3, 8 | 3, 4 | 3, 8 | 2, 7 | 4, 4 | 2, 6 | 4, 4 | 3, 4 |
| 3, 5 | 2, 0 | 3, 5 | 3, 3 | 3, 6 | 3, 6 | 4, 1 | 3, 7 | 4, 1 | 3, 5 |
| 3, 6 | 2, 6 | 3, 6 | 2, 2 | 3, 5 | 3, 0 | 4, 2 | 3, 3 | 4, 2 | 3, 9 |
| 3, 7 | 3, 2 | 3, 7 | 2, 9 | 3, 7 | 2, 4 | 4, 3 | 3, 2 | 4, 3 | 3, 1 |
| 3, 9 | 3, 7 | 3, 9 | 3, 9 | 4, 0 | 3, 1 | 4, 0 | 2, 5 | 4, 0 | 2, 8 |
Вариант 10. Жирность молока некоторых пород крупного рогатого скота (%).
| 4, 1 | 4, 1 | 2, 5 | 2, 0 | 3, 6 | 3, 6 | 3, 3 | 3, 7 | 3, 5 | 3, 5 |
| 3, 5 | 3, 8 | 3, 0 | 4, 1 | 3, 4 | 4, 5 | 4, 1 | 4, 5 | 5, 0 | 2, 3 |
| 4, 2 | 2, 7 | 3, 6 | 2, 6 | 3, 5 | 3, 0 | 2, 2 | 3, 3 | 3, 9 | 3, 6 |
| 3, 1 | 3, 2 | 3, 1 | 4, 2 | 2, 1 | 4, 6 | 4, 2 | 4, 6 | 2, 0 | 2, 7 |
| 2, 8 | 4, 3 | 3, 4 | 3, 2 | 3, 7 | 2, 4 | 2, 9 | 3, 2 | 3, 1 | 3, 7 |
| 2, 5 | 3, 3 | 3, 6 | 4, 3 | 2, 8 | 4, 7 | 4, 3 | 4, 7 | 5, 3 | 3, 3 |
| 4, 4 | 2, 9 | 3, 8 | 3, 7 | 3, 8 | 2, 7 | 3, 4 | 2, 6 | 3, 4 | 3, 8 |
| 2, 6 | 2, 7 | 3, 0 | 4, 4 | 3, 0 | 4, 8 | 4, 4 | 4, 8 | 5, 4 | 3, 8 |
| 4, 0 | 4, 0 | 3, 9 | 3, 7 | 4, 0 | 3, 1 | 3, 9 | 2, 5 | 2, 8 | 3, 9 |
| 3, 2 | 2, 9 | 3, 9 | 4, 0 | 3, 5 | 4, 9 | 4, 3 | 4, 9 | 5, 1 | 3, 6 |
Совокупность вариантов, расположенных в определенной последовательности, составят вариационный ряд. Определите наименьшую и наибольшую величину признака – это лимиты изменчивости. Они показывают, в каких пределах изменяется признак. Однако большое количество вариантов (100), расположенных в один ряд, не дает возможности получить наглядную картину изменчивости признака. Более наглядным является построение сгруппированного ряда. Для этого следует разбить все варианты на группы. Количество групп выбираете произвольно (оптимальное количество – 7 групп). Затем определите величину интервала между группами. С этой целью разделите разницу между наибольшей и наименьшей величиной признака на число групп.
Определив границы группы, распределите все варианты по группам и вычислите среднее значение каждой группы, которое равно сумме крайних вариантов, деленное на 2.
Расположив средние значения групп, в порядке нарастания или убывания, получите сгруппированный вариационный ряд, где роль отдельных вариант выполняют средние значения групп. Затем определите частоту каждой группы, то есть количество значений в этой группе, отражающее распределение вариант по группам. Увидите, что частота групп неодинакова, средние члены вариационного ряда встречаются чаще.
Составьте таблицу: в первый столбик впишите интервалы группы, во второй столбик – средние значения групп, в третий – соответствующую им частоту.
| Интервалы группы | Среднее значение групп (v) | Частота встречаемости варианты (p) |
| 30-32 | ||
| 33-35 | ||
| 36-38 | ||
| 39-41 | ||
| 42-44 | ||
| 45-47 | ||
| 48-50 |
РАБОТА 2.