用样本估计总体---北师大版.ppt

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,2017/5/6,#,1.5.1,用样本估计总体,问题提出,从前面的分析可以知道，当研究一个对象时，如果能得到他们的全部数据（可以看作是总体），我们就可以直接从中分析总体的各种信息,.,如人口普查得到的数据较为全面，从中可以很好地反映对象的重要信息,.,但是，在实际问题中，总体的信息往往不能全部得到，因此我们需要进行抽样调查，从总体中抽取一部分作为样本，并用样本的各种信息来估计总体的情况，包括它的分布和基本数字特征,.,1,、用样本去估计总体，是研究统计问题的一个基本思想,2,、前面我们学过的抽样方法有,:,简单随机抽样、系统抽样、分层抽样。要注意这几种抽样方法的联系与区别。,3,、初中时我们学习过样本的频率分布，包括频数、频率的概念，频数分布表和频数分布直方图的制作。,频率分布,频率分布的表示形式有,：,样本频率分布,表；,样本频率分布,图：,样,本频率分布,条形,图、,样,本频率分布,直方,图,样本频率分布折线图,频率,=,频数,样本容量,估计总体的分布,例,1895,年，在英国伦敦有,106,块男性头盖骨被挖掘出土。经考证，头盖骨的主人死于,1665,1666,年之间的大瘟疫。人类学家分别测量了这些头盖骨的宽度，数据如下所示（单位：,mm,）：,146 141 139 140 145 141 142 131 142 140 144 140,138 139 147 139 141 137 141 132 140 140 141 143,134 146 134 142 133 149 140 140 143 143 149 136,141 143 143 141 138 136 138 144 136 145 143 137,142 146 140 148 140 140 139 139 144 138 146 153,148 152 143 140 141 145 148 139 136 141 140 139,158 135 132 148 142 145 145 121 129 143 148 138,149 146 141 142 144 137 153 148 144 138 150 148,138 145 145 142 143 143 148 141 145 141,请你估计在,16651666,年之间，英国男性头盖骨宽度的分 布情况,.,频数分布表与频率分布表,宽度,/,mm,频数,频率,121,1,0.009,129,1,0.009,131,1,0.009,132,2,0.019,133,1,0.009,134,2,0.019,135,1,0.009,136,4,0.038,137,3,0.028,宽度,/,mm,频数,频率,138,7,0.066,139,7,0.066,140,12,0.113,141,12,0.113,142,7,0.066,143,10,0.094,144,5,0.047,145,8,0.075,146,5,0.047,宽度,/,mm,频数,频率,147,1,0.009,148,8,0.075,149,3,0.028,150,1,0.009,152,2,0.019,153,1,0.009,158,1,0.009,从表格中，我们就能估计出总体大致的分布情况了，如在,16651666,年之间，英国男性头盖骨宽度主要在,136149,mm,之间，,135,mm,以下以及,150,mm,以上所占的比率相对较小等,.,但是，这些关于分布情况的描述仍不够形象，为了得到更为直观的信息，我们可以再将表中的数据按照下面的方式分组：,8,1.,求极差,:(,最大值与最小值的差,),最大值,=,158,最小值,=,121,所以，极,差,158-121,=,37,2.,决定组距与组数,:,当样本容量不超过,1,2,0,时,按照数据的多少,常分成,512,组,.,为方便组距的选择应力,求,“,取,整”,.,本题如果组距,为,5mm,.,则,3.,将数据分组,(,给出组的界限,),所以将数据分,成,8,组,较合适,.,120,125,),125,1,30,),1,30,1,3,5),155,160,),共,8,组,.,步骤：,画频率分布直方图,4.,列出频率分布表,.(,填写频率,/,组距一栏,),5.,画出频率分布直方图,37,5,7.4,宽度分组（,x,i,）,频数（,n,i,）,频率（,f,i,）,f,i,/,x,i,120125,mm,1,0.009,0.0018,125130,mm,1,0.009,0.0018,130135,mm,6,0.057,0.0114,135140,mm,22,0.208,0.0416,140145,mm,46,0.434,00868,145150,mm,25,0.236,0.0472,150155,mm,4,0.038,0.0076,155160,mm,1,0.009,0.0018,频数频率分组表,注意：当数据在,120,个以内时，通常按照数据的多少分成,512,组，在实际操作中，一般要求各组的组距相等,.,0.06,0.08,0.10,0.02,0.04,0,145,宽度,/,150,135,140,160,130,125,120,155,f,i,x,i,0.0018,0.0018,0.0018,0.0076,0.0416,0.0114,0.0472,0.0868,0,10,20,30,40,50,145,宽度,/,150,135,140,160,130,125,120,155,频数,1,1,1,6,4,22,25,46,0.06,0.08,0.10,0.02,0.04,0,145,宽度,/,150,135,140,160,130,125,120,155,频率,组距,0.0018,0.0018,0.0018,0.0076,0.0416,0.0114,0.0472,0.0868,频,率分布直方图,X,轴：,组距,Y,轴,：,频率,组距,0.06,0.08,0.10,0.02,0.04,0,145,宽度,/,mm,150,135,140,160,130,125,120,155,f,i,x,i,0.0018,0.0018,0.0018,0.0076,0.0416,0.0114,0.0472,0.0868,115,165,频率折线图,频率折线图,观察上图，你能知道：,（,1,）头盖骨的宽度位于哪个区间的数据最多？,（,2,）头盖骨的宽度在,140,145,mm,的频率约是多少？,（,3,）头盖骨的宽度在,135,140,mm,的频率约是多少？,（,4,）,头盖骨的宽度小于,140,mm,的频率约是多少,？,（,5,）,头盖骨的宽度在,137,142,mm,的频率约是多少？,140145,0.434,0.208,0.2083/5,0.4342/5,0.2984,0.283,0.06,0.08,0.10,0.02,0.04,0,145,宽度,/,150,135,140,160,130,125,120,155,f,i,x,i,0.0018,0.0018,0.0018,0.0076,0.0416,0.0114,0.0472,0.0868,频,率分布直方图,X,轴：,组距,Y,轴：,频率,组距,图形的意义：,频率分布直方图中各小长方形的面,积,表,示什么？各小长方形的面积之和为多少？,各小长方形的面积之和,=,1,各小长方形的面积,=,*,组距,=,频,率,频率,组距,抽象概括,在上面的例子中，虽然我们是用样本数据的频率分布来估计总体的分布，与真正的总体分布是有差别的，但是当样本量不断增大时，样本中落在每个区间内的样本数的频率会越来越稳定于总体在相应区间内取值的概率,.,也就是说，一般地，,样本容量越大，用样本的频率分布去估计总体的分布就越精确,.,课内练习,一位植物学家想要研究某类植物生长,1,年之后的高度，他随机抽取了,60,株此类植物，测得它们生长,1,年之后的高度如下所示（单位：）：,73 84 91 68 72 83 75 58 87 41 48 61 65 72 92 68 73 43 57 78,80 59 84 42 67 69 64 73 51 65 63 82 90 54 63 76 61 68 66 78,55 81 94 79 45 67 70 98 76 72 72 91 86 75 76 50 69 69 56 74,（,1,）完成下表,:,高度分组（,i,）,频数（,n,i,）,频率（,f,i,）,f,i,/,x,i,4050cm,5060cm,6070cm,7080cm,8090cm,90100cm,5,8,16,17,8,6,0.083,0.133,0.267,0.283,0.133,0.100,0.0083,0.0133,0.0267,0.0283,0.0133,0.0100,0.015,0.02,0.03,0.005,0.01,0,高度,/,50,f,i,x,i,0.025,40,30,60,70,80,90,100,110,（,2,）频率分布直方图,0.015,0.02,0.03,0.005,0.01,0,高度,/,50,f,i,x,i,0.025,40,30,60,70,80,90,100,110,（,2,）频率折线图,超过,50%,的此类植物在生长,1,年之后的高度在,6080cm,之间，,50cm,以下及,90cm,以上所占的比例相对较小,.,90,100,110,120,130,140,分数,频率,0.45,0.05,0.15,1,、某市高三数学抽样考试中，对,90,分以上（含,90,分）的成绩进行统计，其频率分布图如图，若,130,140,分数段的人数为,90,人；则,90,100,分数段的人数为：,；,810,2,、一个容量为,20,的样本数据,.,分组后,.,组距与频数如下：,(0,20 2;(20,30 3,(30,40 4;(40,50 5;(50,60 4;(60,70 2,。则样本在,(,50,上的频率为：,，,7/10,2400,2700,3000,3300,3600,3900,X,体重,y,0.001,3,、观察新生婴儿的体重，其频率分布直方图,如图所示，则新生婴儿体重,(2700,3000),的频,率为：,；,0.3,23,频率分布直方图,画法,频率分布直方图,应用,步骤,1.,求极差,2.,决定组距与组数,3.,将数据分组,4.,列频率分布表,5.,画频率分布直方图,