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Структурные средние. Расчет среднего уровня и дисперсии |
Лекция 6
Лекция 6
Коэффициент вариации V
используется:
1) Для
оценки средней величины.
2) Для
оценки тенденции вариации (неоднородности).
3) Для
сравнения вариации различных явлений
4) Для
оценки равномерности.
Кравн. = 100 – V
Структурные средние
Мо – мода; Ме – медиана.
Мо – значение варьирующего признака, которое
имеет наибольшую частоту.
Мода в дискретном ряду распределения.
Распределение семей города Н по числу детей:
Число детей в
семье, чел.
|
Число семей
|
1
|
50000
|
2
|
30000
|
3
|
5000
|
4
|
700
|
Мода в интервальном ряду распределения с равными
интервалами.
Мо = (XMo + IMo)*(FMo – FMo-1)/((FMo - FMo) + (FMo – FMo+1))
Мода в интервальном ряду распределения с неравными
интервалами
Зарплата у.е. на чел.
|
Удельный вес работников в % к итогу
|
Плотность распределения, m=f/i
|
100-120
|
10
|
0,5
|
120-140
|
30
|
1,5
|
140-180
|
40
|
1,0
|
180-220
|
20
|
0,5
|
Итого
|
100
|
|
Делаем перегруппировку интервалов, чтобы соседние интервалы
с Мо были одинаковыми.
100-120
|
10
|
120-140
|
30
|
140-160
|
20
|
160-180
|
20
|
180-220
|
20
|
Итого
|
100
|
Ме – медианы – величины признака, которые делят
упорядоченную последовательность его значений на две равные по численности
части.
Медиана в дискретном ряду распределения.
Пример:
20 22 28
30 31
Медиана в интервальном ряду распределения
Ме = (XMe + IMe)*(1/2∑f – fнак. до мед интер.)/fлокальное
|
Fлокальное
|
X
|
Fнак.
до инт.
|
До 100
|
2
|
90
|
2
|
100-120
|
10
|
110
|
12
|
120-140
|
32
|
130
|
44
|
140-160
|
36
|
150
|
80
|
Св. 160
|
20
|
170
|
100
|
Итого
|
100
|
|
|
Пример: экономический смысл – половина рабочих имела доход
больше чем Ме, а половина меньше.
Расчет среднего уровня и дисперсии.
|
F
|
X
|
X
- A
|
x’=(X-A)/i
|
x’*f
|
x’2*f
|
До 100
|
2
|
90
|
- 40
|
- 2
|
- 4
|
8
|
100-120
|
10
|
110
|
- 20
|
- 1
|
- 10
|
10
|
120-140
|
32
|
130
|
0
|
0
|
0
|
0
|
140-160
|
36
|
150
|
20
|
1
|
36
|
36
|
Св. 160
|
20
|
170
|
40
|
2
|
40
|
80
|
Итого
|
100
|
|
|
|
62
|
|
Способ моментов основан на
упрощении вариант.
x’=(X-A)/i
Если все варианты уменьшим на среднюю величину,
то все варианты уменьшаться на эту величину.
Если все варианты увеличим в ... раз, то средняя
величина увеличиться в ... раз.
Пусть А = 130, i = 20
__
Mi = X’ = ∑x’*f/∑f
__
X’ = 62/100 = 0,62
_ _
X = X’*i + A = 0,62*20 + 130 =
142,4
σ2 = i2
* (m2 – m12) = 382,24
|
|
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