Реферат: Общая теория статистики
<img src="/cache/referats/6126/image001.gif" " " v:shapes="_x0000_s1026"> <img src="/cache/referats/6126/image002.gif" " " v:shapes="_x0000_s1027"> <img src="/cache/referats/6126/image003.gif" v:shapes="_x0000_s1028"> <img src="/cache/referats/6126/image004.gif" " v:shapes="_x0000_s1029"> <img src="/cache/referats/6126/image005.gif" v:shapes="_x0000_s1030"> <img src="/cache/referats/6126/image006.gif" " " v:shapes="_x0000_s1031"> <img src="/cache/referats/6126/image007.gif" v:shapes="_x0000_s1032"> <img src="/cache/referats/6126/image008.gif" v:shapes="_x0000_s1033"> <img src="/cache/referats/6126/image009.gif" v:shapes="_x0000_s1034">
<span Times New Roman",«serif»; mso-fareast-font-family:«Times New Roman»;mso-ansi-language:RU;mso-fareast-language: RU;mso-bidi-language:AR-SA"><img src="/cache/referats/6126/image010.gif" v:shapes="_x0000_s1164"><img src="/cache/referats/6126/image011.gif" v:shapes="_x0000_s1163"><span Garamond",«serif»">Задание 1.
С цельювыявления зависимости между экономическими показателями провести группировку 50ремонтных предприятий железнодорожного транспорта (см. Таб. 1) с равнымиинтервалами, выделив 5 групп.
<span Garamond",«serif»; mso-ansi-language:EN-US">
<span Garamond",«serif»">Исходные данные:
Таб. 1<span Garamond",«serif»">
<span Garamond",«serif»">№
<span Garamond",«serif»">Группировоч-ный признак
<span Garamond",«serif»">Результатив-ный признак
<span Garamond",«serif»">
<span Garamond",«serif»">
<span Garamond",«serif»">№
<span Garamond",«serif»">Группировоч-ный признак
<span Garamond",«serif»">Результатив-ный признак
<span Garamond",«serif»">число вагонов находящихся в ремонте, шт/сут
<span Garamond",«serif»">чистая прибыль предприятия, млн.руб.
<span Garamond",«serif»">
<span Garamond",«serif»">число вагонов находящихся в ремонте, шт/сут
<span Garamond",«serif»">чистая прибыль предприятия, млн.руб.
<span Garamond",«serif»">51
<span Garamond",«serif»">8
<span Garamond",«serif»">130
<span Garamond",«serif»">
<span Garamond",«serif»">76
<span Garamond",«serif»">10
<span Garamond",«serif»">134
<span Garamond",«serif»">52
<span Garamond",«serif»">11
<span Garamond",«serif»">148
<span Garamond",«serif»">
<span Garamond",«serif»">77
<span Garamond",«serif»">6
<span Garamond",«serif»">136
<span Garamond",«serif»">53
<span Garamond",«serif»">36
<span Garamond",«serif»">155
<span Garamond",«serif»">
<span Garamond",«serif»">78
<span Garamond",«serif»">7
<span Garamond",«serif»">133
<span Garamond",«serif»">54
<span Garamond",«serif»">2
<span Garamond",«serif»">124
<span Garamond",«serif»">
<span Garamond",«serif»">79
<span Garamond",«serif»">1
<span Garamond",«serif»">127
<span Garamond",«serif»">55
<span Garamond",«serif»">2
<span Garamond",«serif»">125
<span Garamond",«serif»">
<span Garamond",«serif»">80
<span Garamond",«serif»">7
<span Garamond",«serif»">128
<span Garamond",«serif»">56
<span Garamond",«serif»">29
<span Garamond",«serif»">135
<span Garamond",«serif»">
<span Garamond",«serif»">81
<span Garamond",«serif»">1
<span Garamond",«serif»">118
<span Garamond",«serif»">57
<span Garamond",«serif»">14
<span Garamond",«serif»">126
<span Garamond",«serif»">
<span Garamond",«serif»">82
<span Garamond",«serif»">5
<span Garamond",«serif»">124
<span Garamond",«serif»">58
<span Garamond",«serif»">14
<span Garamond",«serif»">136
<span Garamond",«serif»">
<span Garamond",«serif»">83
<span Garamond",«serif»">15
<span Garamond",«serif»">137
<span Garamond",«serif»">59
<span Garamond",«serif»">8
<span Garamond",«serif»">124
<span Garamond",«serif»">
<span Garamond",«serif»">84
<span Garamond",«serif»">6
<span Garamond",«serif»">110
<span Garamond",«serif»">60
<span Garamond",«serif»">8
<span Garamond",«serif»">128
<span Garamond",«serif»">
<span Garamond",«serif»">85
<span Garamond",«serif»">17
<span Garamond",«serif»">139
<span Garamond",«serif»">61
<span Garamond",«serif»">5
<span Garamond",«serif»">110
<span Garamond",«serif»">
<span Garamond",«serif»">86
<span Garamond",«serif»">8
<span Garamond",«serif»">148
<span Garamond",«serif»">62
<span Garamond",«serif»">8
<span Garamond",«serif»">150
<span Garamond",«serif»">
<span Garamond",«serif»">87
<span Garamond",«serif»">1
<span Garamond",«serif»">123
<span Garamond",«serif»">63
<span Garamond",«serif»">1
<span Garamond",«serif»">110
<span Garamond",«serif»">
<span Garamond",«serif»">88
<span Garamond",«serif»">10
<span Garamond",«serif»">138
<span Garamond",«serif»">64
<span Garamond",«serif»">6
<span Garamond",«serif»">122
<span Garamond",«serif»">
<span Garamond",«serif»">89
<span Garamond",«serif»">21
<span Garamond",«serif»">189
<span Garamond",«serif»">65
<span Garamond",«serif»">18
<span Garamond",«serif»">140
<span Garamond",«serif»">
<span Garamond",«serif»">90
<span Garamond",«serif»">11
<span Garamond",«serif»">139
<span Garamond",«serif»">66
<span Garamond",«serif»">4
<span Garamond",«serif»">110
<span Garamond",«serif»">
<span Garamond",«serif»">91
<span Garamond",«serif»">2
<span Garamond",«serif»">122
<span Garamond",«serif»">67
<span Garamond",«serif»">9
<span Garamond",«serif»">139
<span Garamond",«serif»">
<span Garamond",«serif»">92
<span Garamond",«serif»">2
<span Garamond",«serif»">124
<span Garamond",«serif»">68
<span Garamond",«serif»">2
<span Garamond",«serif»">121
<span Garamond",«serif»">
<span Garamond",«serif»">93
<span Garamond",«serif»">1
<span Garamond",«serif»">113
<span Garamond",«serif»">69
<span Garamond",«serif»">1
<span Garamond",«serif»">111
<span Garamond",«serif»">
<span Garamond",«serif»">94
<span Garamond",«serif»">8
<span Garamond",«serif»">117
<span Garamond",«serif»">70
<span Garamond",«serif»">5
<span Garamond",«serif»">132
<span Garamond",«serif»">
<span Garamond",«serif»">95
<span Garamond",«serif»">6
<span Garamond",«serif»">126
<span Garamond",«serif»">71
<span Garamond",«serif»">1
<span Garamond",«serif»">129
<span Garamond",«serif»">
<span Garamond",«serif»">96
<span Garamond",«serif»">3
<span Garamond",«serif»">130
<span Garamond",«serif»">72
<span Garamond",«serif»">7
<span Garamond",«serif»">139
<span Garamond",«serif»">
<span Garamond",«serif»">97
<span Garamond",«serif»">3
<span Garamond",«serif»">112
<span Garamond",«serif»">73
<span Garamond",«serif»">9
<span Garamond",«serif»">148
<span Garamond",«serif»">
<span Garamond",«serif»">98
<span Garamond",«serif»">2
<span Garamond",«serif»">133
<span Garamond",«serif»">74
<span Garamond",«serif»">25
<span Garamond",«serif»">144
<span Garamond",«serif»">
<span Garamond",«serif»">99
<span Garamond",«serif»">25
<span Garamond",«serif»">195
<span Garamond",«serif»">75
<span Garamond",«serif»">16
<span Garamond",«serif»">146
<span Garamond",«serif»">
<span Garamond",«serif»">100
<span Garamond",«serif»">5
<span Garamond",«serif»">176
<span Garamond",«serif»; mso-ansi-language:EN-US">
<span Garamond",«serif»">Решение задачи:
<span Garamond",«serif»;mso-fareast-font-family: Garamond;mso-bidi-font-family:Garamond">1.<span Times New Roman"">
<span Garamond",«serif»">Группировкапроизводится по группировочному признаку. Определим величину (шаг) интервалагруппировки по формуле:<img src="/cache/referats/6126/image012.gif" v:shapes="_x0000_s1135"><span Garamond",«serif»; mso-ansi-language:EN-US">
<span Garamond",«serif»; mso-ansi-language:EN-US"><img src="/cache/referats/6126/image014.gif" v:shapes="_x0000_i1025">
<span Garamond",«serif»;mso-ansi-language:EN-US"><span Garamond",«serif»; mso-ansi-language:EN-US">
<img src="/cache/referats/6126/image015.gif" v:shapes="_x0000_s1166"><img src="/cache/referats/6126/image016.gif" v:shapes="_x0000_s1165"><span Garamond",«serif»; mso-ansi-language:EN-US">k
<span Garamond",«serif»"> = 5, число групп в группировке (изусловия)<span Garamond",«serif»;mso-ansi-language:EN-US"><span Garamond",«serif»; mso-ansi-language:EN-US">Xmax, Xmin
<span Garamond",«serif»"> – максимальное иминимальное значение группировочного<span Garamond",«serif»"> признака
<span Garamond",«serif»">
<span Garamond",«serif»;mso-ansi-language: EN-US">l<span Garamond",«serif»"> – величина (шаг) интервала группировки.<img src="/cache/referats/6126/image017.gif" v:shapes="_x0000_s1136"><span Garamond",«serif»; mso-ansi-language:EN-US">
<span Garamond",«serif»; mso-ansi-language:EN-US"><img src="/cache/referats/6126/image019.gif" v:shapes="_x0000_i1026">
<span Garamond",«serif»">
<span Garamond",«serif»;mso-fareast-font-family: Garamond;mso-bidi-font-family:Garamond">2.<span Times New Roman"">
<span Garamond",«serif»">Определимнижнюю и верхнюю интервальные границы для каждой группы:<span Garamond",«serif»"> номер границы
<span Garamond",«serif»"> группы нижняя верхняя
<span Garamond",«serif»"> 1 1.0 8.0
<span Garamond",«serif»"> 2 8.0 15.0
<span Garamond",«serif»"> 3 15.0 22.0
<span Garamond",«serif»"> 4 22.0 29.0
<span Garamond",«serif»"> 5 29.0 36.0
<span Garamond",«serif»; mso-ansi-language:EN-US">
<span Garamond",«serif»; mso-ansi-language:EN-US">
<span Garamond",«serif»;mso-fareast-font-family: Garamond;mso-bidi-font-family:Garamond">3.<span Times New Roman"">
<span Garamond",«serif»">Составимрабочую таблицу, куда сведем первичный статистический материал:<span Garamond",«serif»">
<span Garamond",«serif»">Группы предпри-ятий по кол-ву вагонов нахощящ. на ремонте, шт/сут
<span Garamond",«serif»">
<span Garamond",«serif»">Номер предприятия
<span Garamond",«serif»">Число вагонов, находящихся в ремонте, шт/сут
<span Garamond",«serif»">Чистая прибыль предприятия, млн.руб.
<span Garamond",«serif»"> 1
<span Garamond",«serif»"> 2
<span Garamond",«serif»"> 3
<span Garamond",«serif»"> 4
<span Garamond",«serif»"> 1.0 — 8.0
<span Garamond",«serif»">51
<span Garamond",«serif»">54
<span Garamond",«serif»">55
<span Garamond",«serif»">59
<span Garamond",«serif»">60
<span Garamond",«serif»">61
<span Garamond",«serif»">62
<span Garamond",«serif»">63
<span Garamond",«serif»">64
<span Garamond",«serif»">66
<span Garamond",«serif»">68
<span Garamond",«serif»">69
<span Garamond",«serif»">70
<span Garamond",«serif»">71
<span Garamond",«serif»">72
<span Garamond",«serif»">77
<span Garamond",«serif»">78
<span Garamond",«serif»">79
<span Garamond",«serif»">80
<span Garamond",«serif»">81
<span Garamond",«serif»">82
<span Garamond",«serif»">84
<span Garamond",«serif»">86
<span Garamond",«serif»">87
<span Garamond",«serif»">91
<span Garamond",«serif»">92
<span Garamond",«serif»">93
<span Garamond",«serif»">94
<span Garamond",«serif»">95
<span Garamond",«serif»">96
<span Garamond",«serif»">97
<span Garamond",«serif»">98
<span Garamond",«serif»">100
<span Garamond",«serif»">8
<span Garamond",«serif»">2
<span Garamond",«serif»">2
<span Garamond",«serif»">8
<span Garamond",«serif»">6
<span Garamond",«serif»">5
<span Garamond",«serif»">8
<span Garamond",«serif»">1
<span Garamond",«serif»">6
<span Garamond",«serif»">4
<span Garamond",«serif»">2
<span Garamond",«serif»">1
<span Garamond",«serif»">5
<span Garamond",«serif»">1
<span Garamond",«serif»">7
<span Garamond",«serif»">6
<span Garamond",«serif»">7
<span Garamond",«serif»">1
<span Garamond",«serif»">7
<span Garamond",«serif»">1
<span Garamond",«serif»">5
<span Garamond",«serif»">6
<span Garamond",«serif»">8
<span Garamond",«serif»">1
<span Garamond",«serif»">2
<span Garamond",«serif»">2
<span Garamond",«serif»">1
<span Garamond",«serif»">8
<span Garamond",«serif»">6
<span Garamond",«serif»">3
<span Garamond",«serif»">3
<span Garamond",«serif»">2
<span Garamond",«serif»">5
<span Garamond",«serif»">130
<span Garamond",«serif»">124
<span Garamond",«serif»">125
<span Garamond",«serif»">124
<span Garamond",«serif»">128
<span Garamond",«serif»">110
<span Garamond",«serif»">150
<span Garamond",«serif»">110
<span Garamond",«serif»">122
<span Garamond",«serif»">110
<span Garamond",«serif»">121
<span Garamond",«serif»">111
<span Garamond",«serif»">132
<span Garamond",«serif»">129
<span Garamond",«serif»">139
<span Garamond",«serif»">136
<span Garamond",«serif»">133
<span Garamond",«serif»">127
<span Garamond",«serif»">128
<span Garamond",«serif»">118
<span Garamond",«serif»">124
<span Garamond",«serif»">110
<span Garamond",«serif»">148
<span Garamond",«serif»">123
<span Garamond",«serif»">122
<span Garamond",«serif»">124
<span Garamond",«serif»">113
<span Garamond",«serif»">117
<span Garamond",«serif»">126
<span Garamond",«serif»">130
<span Garamond",«serif»">112
<span Garamond",«serif»">133
<span Garamond",«serif»">176
<span Garamond",«serif»">ИТОГО :
<span Garamond",«serif»"> 33
<span Garamond",«serif»">140
<span Garamond",«serif»">4165
<span Garamond",«serif»">
<span Garamond",«serif»">8.0 - 15.0
<span Garamond",«serif»">
<span Garamond",«serif»">52
<span Garamond",«serif»">57
<span Garamond",«serif»">58
<span Garamond",«serif»">67
<span Garamond",«serif»">73
<span Garamond",«serif»">76
<span Garamond",«serif»">83
<span Garamond",«serif»">88
<span Garamond",«serif»">90
<span Garamond",«serif»">
<span Garamond",«serif»">11
<span Garamond",«serif»">14
<span Garamond",«serif»">14
<span Garamond",«serif»">9
<span Garamond",«serif»">9
<span Garamond",«serif»">10
<span Garamond",«serif»">15
<span Garamond",«serif»">10
<span Garamond",«serif»">11
<span Garamond",«serif»">
<span Garamond",«serif»">148
<span Garamond",«serif»">126
<span Garamond",«serif»">136
<span Garamond",«serif»">139
<span Garamond",«serif»">148
<span Garamond",«serif»">134
<span Garamond",«serif»">137
<span Garamond",«serif»">138
<span Garamond",«serif»">139
<span Garamond",«serif»">ИТОГО :
<span Garamond",«serif»"> 9
<span Garamond",«serif»">103
<span Garamond",«serif»">1245
<span Garamond",«serif»">
<span Garamond",«serif»">15.0 - 22.0
<span Garamond",«serif»">
<span Garamond",«serif»">65
<span Garamond",«serif»">75
<span Garamond",«serif»">85
<span Garamond",«serif»">89
<span Garamond",«serif»">
<span Garamond",«serif»">18
<span Garamond",«serif»">16
<span Garamond",«serif»">17
<span Garamond",«serif»">21
<span Garamond",«serif»">
<span Garamond",«serif»">140
<span Garamond",«serif»">146
<span Garamond",«serif»">139
<span Garamond",«serif»">189
<span Garamond",«serif»">ИТОГО :
<span Garamond",«serif»"> 4
<span Garamond",«serif»">72
<span Garamond",«serif»">614
<span Garamond",«serif»">
<span Garamond",«serif»">22.0 - 29.0
<span Garamond",«serif»">
<span Garamond",«serif»">56
<span Garamond",«serif»">74
<span Garamond",«serif»">99
<span Garamond",«serif»">
<span Garamond",«serif»">29
<span Garamond",«serif»">25
<span Garamond",«serif»">25
<span Garamond",«serif»">
<span Garamond",«serif»">135
<span Garamond",«serif»">144
<span Garamond",«serif»">195
<span Garamond",«serif»">ИТОГО :
<span Garamond",«serif»"> 3
<span Garamond",«serif»">79
<span Garamond",«serif»">474
<span Garamond",«serif»">
<span Garamond",«serif»">29.0 - 36.0
<span Garamond",«serif»">
<span Garamond",«serif»">53
<span Garamond",«serif»">
<span Garamond",«serif»">36
<span Garamond",«serif»">
<span Garamond",«serif»">155
<span Garamond",«serif»">ИТОГО :
<span Garamond",«serif»"> 1
<span Garamond",«serif»">36
<span Garamond",«serif»">155
<span Garamond",«serif»; mso-ansi-language:EN-US">
<span Garamond",«serif»; mso-ansi-language:EN-US">
<span Garamond",«serif»;mso-fareast-font-family: Garamond;mso-bidi-font-family:Garamond">4.<span Times New Roman"">
<span Garamond",«serif»">Разработаеманалитическую таблицу взаимосвязи между числом вагонов находящихся на ремонте ичистой прибылью : <img src="/cache/referats/6126/image020.gif" v:shapes="_x0000_s1168">Табл. 2
<span Garamond",«serif»">Группы предпр. по кол-ву вагонов поступающих в ремонт
<span Garamond",«serif»">Число предпри-ятий
<span Garamond",«serif»">Число вагонов находящихся в ремонте, шт/сут
Чистая прибыль, млн.руб<span Garamond",«serif»">Всего по группе
<span Garamond",«serif»">в среднем на одно предприятие
<span Garamond",«serif»">Всего по группе
<span Garamond",«serif»">в среднем на одно предприятие
<span Garamond",«serif»"> 1.0 - 8.0
<span Garamond",«serif»">33
<span Garamond",«serif»">140
<span Garamond",«serif»">4,2
<span Garamond",«serif»">4165
<span Garamond",«serif»">126,2
<span Garamond",«serif»"> 8.0 — 15.0
<span Garamond",«serif»">9
<span Garamond",«serif»">103
<span Garamond",«serif»">11,4
<span Garamond",«serif»">1245
<span Garamond",«serif»">138,3
<span Garamond",«serif»">15.0 - 22.0
<span Garamond",«serif»">4
<span Garamond",«serif»">72
<span Garamond",«serif»">18,0
<span Garamond",«serif»">614
<span Garamond",«serif»">153,5
<span Garamond",«serif»">22.0 - 29.0
<span Garamond",«serif»">3
<span Garamond",«serif»">79
<span Garamond",«serif»">26,3
<span Garamond",«serif»">474
<span Garamond",«serif»">158,0
<span Garamond",«serif»">29.0 - 36.0
<span Garamond",«serif»">1
<span Garamond",«serif»">36
<span Garamond",«serif»">36,0
<span Garamond",«serif»">155
<span Garamond",«serif»">155,0
Исследовавпоказатели работы 50-ти предприятий железнодорожного транспорта, можно сказать,что чистая прибыль предприятия находится в прямой зависимости от числа вагоновнаходящихся в ремонте.
Задание 2.
Рассчитать коэффициенты вариации по группировочномупризнаку на основании исходных данных и по аналитической группировке согласносвоего варианта из задания 1. Объяснить (если есть) расхождения в значенияхполученных коэффициентов.
Решение:
Расчет коэффициента вариации проводится по следующейформуле:
<img src="/cache/referats/6126/image021.gif" v:shapes="_x0000_s1137"><span Garamond",«serif»; mso-ansi-language:EN-US">
<span Garamond",«serif»; mso-ansi-language:EN-US"><img src="/cache/referats/6126/image023.gif" v:shapes="_x0000_i1027">
<span Garamond",«serif»; mso-ansi-language:EN-US">
<span Garamond",«serif»; mso-ansi-language:EN-US">где: G
<span Garamond",«serif»">– среднее квадратическое отклонение;<span Garamond",«serif»">
<span Garamond",«serif»; mso-ansi-language:EN-US">x - <span Garamond",«serif»">средняя величина<img src="/cache/referats/6126/image024.gif" v:shapes="_x0000_s1139"><span Garamond",«serif»">
<span Garamond",«serif»; mso-ansi-language:EN-US">1) <img src="/cache/referats/6126/image026.gif" v:shapes="_x0000_i1028">
<span Garamond",«serif»; mso-ansi-language:EN-US">
<span Garamond",«serif»; mso-ansi-language:EN-US">n
<span Garamond",«serif»"> – объем (или численность) совокупности,<span Garamond",«serif»">х- варианта или значение признака (дляинтервального ряда принимается
<span Garamond",«serif»"> среднее значение)
<span Garamond",«serif»"> Рассчитаем показатели вариации дляпримера, рассмотренного в задании 1. Расчет проводится по группировочномупризнаку. Во-первых, рассчитаем все показатели по исх. данным (см. табл. 1):
<span Garamond",«serif»; mso-ansi-language:EN-US">
<img src="/cache/referats/6126/image027.gif" v:shapes="_x0000_s1169"><span Garamond",«serif»; mso-ansi-language:EN-US"><img src="/cache/referats/6126/image029.gif" v:shapes="_x0000_i1029">
<span Garamond",«serif»; mso-ansi-language:EN-US">
<span Garamond",«serif»">2)Среднее кв. отклонение рассчитываем по формуле:
<img src="/cache/referats/6126/image030.gif" v:shapes="_x0000_s1042"><span Garamond",«serif»; mso-ansi-language:EN-US">
<span Garamond",«serif»"><span Garamond",«serif»; mso-ansi-language:EN-US"> <img src="/cache/referats/6126/image032.gif" v:shapes="_x0000_i1030">
<span Garamond",«serif»; mso-ansi-language:EN-US">
<span Garamond",«serif»"><img src="/cache/referats/6126/image034.gif" v:shapes="_x0000_i1031">
<span Garamond",«serif»">вернемсяк форм. ( 1 )
<span Garamond",«serif»;mso-ansi-language:EN-US"> <span Garamond",«serif»"><img src="/cache/referats/6126/image036.gif" v:shapes="_x0000_i1032">3) Теперь рассчитаем коэффициент вариации поаналитической таблице (см. табл. 2)
<span Garamond",«serif»"> Рассчитаем серединные значенияинтервалов:
<span Garamond",«serif»">
<span Garamond",«serif»"> 4,5 11,5 18.5 25,5 32,5
<img src="/cache/referats/6126/image037.gif" v:shapes="_x0000_s1048 _x0000_s1050 _x0000_s1052 _x0000_s1053 _x0000_s1054 _x0000_s1055 _x0000_s1056 _x0000_s1057 _x0000_s1058 _x0000_s1059 _x0000_s1061 _x0000_s1062"><span Garamond",«serif»">
<span Garamond",«serif»">1 8 15 22 29 36
<img src="/cache/referats/6126/image038.gif" v:shapes="_x0000_s1140"><span Garamond",«serif»;mso-ansi-language: EN-US">
<span Garamond",«serif»;mso-ansi-language: EN-US"><img src="/cache/referats/6126/image040.gif" v:shapes="_x0000_i1033">
<span Garamond",«serif»">, <span Garamond",«serif»">гдеf- частота, т.е. число, которое показывает,сколько встречается каждая
варианта:
<img src="/cache/referats/6126/image042.gif" v:shapes="_x0000_i1034"> ваг.
<span Times New Roman",«serif»">Расчетсреднего квадратического отклонения по аналитической группировке:
<img src="/cache/referats/6126/image043.gif" v:shapes="_x0000_s1141"><span Times New Roman",«serif»">
<img src="/cache/referats/6126/image045.gif" v:shapes="_x0000_i1035">
<img src="/cache/referats/6126/image047.gif" v:shapes="_x0000_i1036">
<img src="/cache/referats/6126/image049.gif" v:shapes="_x0000_i1037">
<img src="/cache/referats/6126/image050.gif" v:shapes="_x0000_s1170">Вывод: в обоих случаях расчета, коэффициент вариации (V)значительно больше 30 %. Следовательно, рассмотренная совокупность неоднороднаи средняя для нее недостаточно типична.
Задание 3.
<span Times New Roman",«serif»">Провести20 % механическую выборку из генеральной совокупности, представленной в таблице(использовать все 100 предприятий), по показателю, который являетсярезультативным признаком в аналитической группировке задания 1 в соответствии свариантом. С вероятностью 0,997 рассчитать границы изменения средней величины вгенеральной совокупности. Рассчитать среднюю данного признака по генеральнойсовокупности (по табл.) и сравнить с результатом, полученным на основаниирасчета по выборочной совокупности. Начало отбора начинать с номера предприятиясовпадающего с номером варианта (8).
<span Times New Roman",«serif»;mso-ansi-language:EN-US"><span Times New Roman",«serif»; mso-ansi-language:EN-US">
1) Табл.<span Times New Roman",«serif»">Номер
<span Times New Roman",«serif»">предприятия
<span Times New Roman",«serif»">Чистая прибыль
<span Times New Roman",«serif»">предпр., млн.руб.
<span Times New Roman",«serif»">
<span Times New Roman",«serif»">Номер
<span Times New Roman",«serif»">предприятия
<span Times New Roman",«serif»">Чистая прибыль
<span Times New Roman",«serif»">предпр., млн.руб.
<span Times New Roman",«serif»">1
<span Times New Roman",«serif»">2
<span Times New Roman",«serif»">
<span Times New Roman",«serif»">1
<span Times New Roman",«serif»">2
<span Times New Roman",«serif»">8
<span Times New Roman",«serif»">13
<span Times New Roman",«serif»">18
<span Times New Roman",«serif»">23
<span Times New Roman",«serif»">28
<span Times New Roman",«serif»">33
<span Times New Roman",«serif»">38
<span Times New Roman",«serif»">43
<span Times New Roman",«serif»">48
<span Times New Roman",«serif»">203
<span Times New Roman",«serif»">163
<span Times New Roman",«serif»">131
<span Times New Roman",«serif»">134
<span Times New Roman",«serif»">130
<span Times New Roman",«serif»">117
<span Times New Roman",«serif»">133
<span Times New Roman",«serif»">125
<span Times New Roman",«serif»">141
<span Times New Roman",«serif»">
<span Times New Roman",«serif»">
<span Times New Roman",«serif»">53
<span Times New Roman",«serif»">58
<span Times New Roman",«serif»">63
<span Times New Roman",«serif»">68
<span Times New Roman",«serif»">73
<span Times New Roman",«serif»">78
<span Times New Roman",«serif»">83
<span Times New Roman",«serif»">88
<span Times New Roman",«serif»">93
<span Times New Roman",«serif»">98
<span Times New Roman",«serif»">155
<span Times New Roman",«serif»">136
<span Times New Roman",«serif»">110
<span Times New Roman",«serif»">121
<span Times New Roman",«serif»">148
<span Times New Roman",«serif»">133
<span Times New Roman",«serif»">137
<span Times New Roman",«serif»">138
<span Times New Roman",«serif»">113
<span Times New Roman",«serif»">133
<span Times New Roman",«serif»">
<span Times New Roman",«serif»">2)Для расчета границ изменения средней характеристики генеральной совокупности поматериалам выборки воспользуемся формулами:
<img src="/cache/referats/6126/image051.gif" v:shapes="_x0000_s1142"><span Times New Roman",«serif»">
<span Times New Roman",«serif»"><img src="/cache/referats/6126/image053.gif" v:shapes="_x0000_i1038">
<span Times New Roman",«serif»">( 1 )<img src="/cache/referats/6126/image054.gif" v:shapes="_x0000_s1143"><span Times New Roman",«serif»">
<span Times New Roman",«serif»"><img src="/cache/referats/6126/image056.gif" v:shapes="_x0000_i1039"> ( 2 )
<img src="/cache/referats/6126/image057.gif" v:shapes="_x0000_s1144"><span Times New Roman",«serif»">
<span Times New Roman",«serif»"><img src="/cache/referats/6126/image059.gif" v:shapes="_x0000_i1040"> ( 3 )
<span Times New Roman",«serif»">
<span Times New Roman",«serif»">Х –средняя генеральной совокупности;
<span Times New Roman",«serif»">Х –средняя выборочной совокупности;
<span Times New Roman",«serif»">-<span Times New Roman"">
<img src="/cache/referats/6126/image060.gif" v:shapes="_x0000_s1171"><img src="/cache/referats/6126/image061.gif" v:shapes="_x0000_s1079"><span Times New Roman",«serif»">предельная ошибка выборки;<span Times New Roman",«serif»; mso-ansi-language:EN-US">
<span Times New Roman",«serif»; mso-ansi-language:EN-US">t - коэффициент доверия = 0,997 (по условию);
<span Times New Roman",«serif»; mso-ansi-language:EN-US">М – средняяошибки выборки
<span Times New Roman",«serif»; mso-ansi-language:EN-US">G2 –
<span Times New Roman",«serif»">дисперсияисследуемого показателя;<span Times New Roman",«serif»; mso-ansi-language:EN-US">n
<span Times New Roman",«serif»">– объем выборочной совокупности;<span Times New Roman",«serif»; mso-ansi-language:EN-US">N –
<span Times New Roman",«serif»">объем генеральной совокупности;<span Times New Roman",«serif»; mso-ansi-language:EN-US">n/N – доля выборочной совокупности в объемегенеральной (или %
<span Times New Roman",«serif»; mso-ansi-language:EN-US"> отбора, выраженный в коэффициенте)
<span Times New Roman",«serif»; mso-ansi-language:EN-US">
Решение:
<span Times New Roman",«serif»;mso-ansi-language:EN-US">1)<span Times New Roman"">
<span Times New Roman",«serif»; mso-ansi-language:EN-US">В данном варианте задания средняя чистая прибыль наодно предприятие по выборочной совокупности равна<span Times New Roman",«serif»; mso-ansi-language:EN-US"> Х=136,8млн.руб.;
<span Times New Roman",«serif»;mso-ansi-language:EN-US">2)<span Times New Roman"">
<span Times New Roman",«serif»; mso-ansi-language:EN-US">дисперсия равна = 407,46;<span Times New Roman",«serif»;mso-ansi-language:EN-US">3)<span Times New Roman"">
<span Times New Roman",«serif»">коэф-тдоверия =3, т.к. вероятность определения границ средней равна =0,997 (по усл);<span Times New Roman",«serif»;mso-ansi-language:EN-US"><span Times New Roman",«serif»;mso-ansi-language:EN-US">4)<span Times New Roman"">
<span Times New Roman",«serif»; mso-ansi-language:EN-US">n/N<span Times New Roman",«serif»">= 0,2, т.к. процент отбора составляет 20 % (по условию).<span Times New Roman",«serif»;mso-ansi-language:EN-US"><span Times New Roman",«serif»;mso-ansi-language:EN-US">5)<span Times New Roman"">
<span Times New Roman",«serif»">Рассчитаемсреднюю ошибку по ф. (3):<span Times New Roman",«serif»; mso-ansi-language:EN-US"><span Times New Roman",«serif»">
<span Times New Roman",«serif»"> <img src="/cache/referats/6126/image063.gif" v:shapes="_x0000_i1041">
<span Times New Roman",«serif»; mso-ansi-language:EN-US"><span Times New Roman",«serif»; mso-ansi-language:EN-US">
<span Times New Roman",«serif»;mso-ansi-language:EN-US">6)<span Times New Roman"">
<span Times New Roman",«serif»; mso-ansi-language:EN-US">Рассчитаем предельную ошибку и определим границыизменения средней по ф. (2)<span Times New Roman",«serif»; mso-ansi-language:EN-US">
<span Times New Roman",«serif»;mso-ansi-language:EN-US"><img src="/cache/referats/6126/image065.gif" v:shapes="_x0000_i1042">
<span