高中数学 (总体分布的估计)课件 苏教版必修3 课件.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,*,*,总体,分布,的估计,学习目标,：,理解频数、频率、样本频,率分布和总体分布等的概念；,掌握频数、样本容量和频,率之间的等量关系；,会用样本频率分布估计总,体分布,.,关于“频数、频率”,在一定条件下事件,A,在抽样中,出现的,次数,叫做事件,A,出现的,频数,.,事件,A,的,频数,在样本中,所占的,比率,称为事件,A,抽样中出现的,频率,.,频率是不超过,1,的非负数有理数,.,一个容量为,40,的样本，把它分成,6,组，第一组到第四组的频数分别为,5,6,7,10.,第五组的频率是,0.2,，则第六组的,频数是,，频率是,.,4,0.1,例题,为了了解某校学生视力状况，该校校医在上,学期每月抽检一次，并统计两眼视力均在,0.8,以上,的学生人数,.,由于某种原因，记载表中某些数,据丢失,(,见下表,),，请同学们帮助复原此表,.,例题,抽样序号,频 数,样本容量,频 率,1(02、9),62,100,2(02、10),48,0.60,3(02、11),200,0.61,4(02、12),30,50,5(03、1),90,0.59,0.62,0.60,80,122,53,关于“频率分布”,根据所抽取样本的大小，分别,计算某一事件出现的频率，这些,频,率的分布规律,(,取值状况,),，叫做样本的,频率分布,.,通常将,样本的容量,、样本中出现该,事件的频数,以及计算所得的,相应频率,列,在一张表中，叫做,样本频率分布表,.(,一,般由以下,四个部分：序号、样本容量、,事件的频数、事件的频率,),也就是说,频率分布,即,频率规律,又如：在稳定的生产条件下，把一定时期,内某种产品的全部当做总体，从中抽取,n,件,(,即,相当于做,n,次试验,),，考虑到次品的情况,.,记在,n,件产品中抽取,m,件次品，则,m,叫次品出现的频,数,，次品数,m,占所抽的产品件数,n,的,比率 称为,产品抽验中次品出现的频率,.,显然,的取值范围,是 中有理数组成的集合,.,在上述产品抽样中，对应所抽取的不同样,本,(,容量为,n,),，,根据实际抽取时的记录结果，,可编制出相应的频率分布表如下：,抽样,序号,n,=25,n,=25,0,n,=2500,m,m,/,n,m,m,/,n,m,m,/,n,1,1,0.04,12,0.048,157,0.0628,2,4,0.16,14,0.056,152,0.0608,3,0,0.00,17,0.068,157,0.0628,4,0,0.00,11,0.044,136,0.0544,5,1,0.04,22,0.088,152,0.0608,6,1,0.04,9,0.036,135,0.0540,7,2,0.08,15,0.060,143,0.0572,8,0,0.00,14,0.056,160,0.0640,9,1,0.04,21,0.084,149,0.0596,10,1,0.04,8,0.032,153,0.0612,在,实际问题中，如果,总体容量较小且统,计项目较少,时，常根据实际抽取时的记录结,果，,编制出如上所示的频率分布表,.,在实际问题中，如果,总体容量较大或统,计项目较多,时，常根据实际抽取时的记录结,果，编制出,如课本,P,12,的频率分布表,.,抽样,序号,n,=,25,n,=,25,0,n,=,2500,m,m,/,n,m,m,/,n,m,m,/,n,1,1,0.04,12,0.048,157,0.0628,2,4,0.16,14,0.056,152,0.0608,3,0,0.00,17,0.068,157,0.0628,4,0,0.00,11,0.044,136,0.0544,5,1,0.04,22,0.088,152,0.0608,6,1,0.04,9,0.036,135,0.0540,7,2,0.08,15,0.060,143,0.0572,8,0,0.00,14,0.056,160,0.0640,9,1,0.04,21,0.084,149,0.0596,10,1,0.04,8,0.032,153,0.0612,在稳定的生产条件下，把一定时期内某种产品的全部当,做总体，从中抽取,n,件产品，考虑到次品的情况,.,记在,n,件产,品中出现,m,件次品，,根据实际抽取记录结果，编制出相应的,频率分布表如下：,注意到本例中，,次品频率总是是,0.06,附近摆动,，说明,出现次品的概率为,0.06,，,因此，可以得到下表：,试验结果,概率,次品,(,可以用,0,表示,),0.06,正品,(,可以用,1,表示,),0.94,这张表反映了总体取值的概率分布规律,取,0,的概率为,0.06,，取,1,的概率为,0.94.,这种总体取值的概率分布规律通常称为总,体概率分布，简称总体分布,.,关于“总体分布”,总体取值的概率分布规律,，通常,称为总体概率分布，简称,总体分布,.,试 验 结 果,概 率,0.8,以上,(,可以用,1,表示,),0.06,非,0.8,以上,(,可以用,0,表示,),0.94,总体分布可列表表示,，如上述视力,检查抽样中的总体分布如下表：,总体分布的估计：,在实践中，往往是从,总体中抽取一个样本，,用样本的频率分布去,估计总体,(,概率,),分布,.,一般地，样本容量越大，,这种估计就越精确,.,四、关于“总体分布的估计”,试 验 结 果,概 率,次品,(,可以用,0,表示,),0.06,正品,(,可以用,1,表示,),0.94,总体,(,概率,),分布的估计：,在实践中，往,往是从总体中抽取一个样本，,用样本的频,率分布去估计总体,(,概率,),分布,.,一般地，样,本容量越大，这种估计就越精确,.,上述产品抽样中，即通过这种方法对,总体分布估计，并得到下表：,有一个容量为,50,的样本，数据的分组及,各组的频数如下：,12.5,15.5)3,24.5,27.5)10,15.5,18.5)8,27.5,30.5)5,18.5,21.5)9,30.5,33.5)4,21.5,24.5)11,(1),列出样本的频率分布表；,(2),根据频率分布表估计，数据落在,15.5,24.5,),的概率约是多少？,分 组,频 数,频 率,合 计,数据落在,15.5,24.5),的概率约是,0.56.,15.5,18.5),8,0.16,18.5,21.5),9,0.18,21.5,24.5),11,0.22,12.5,15.5),3,0.06,15.5,18.5),8,0.16,18.5,21.5),9,0.18,21.5,24.5),11,0.22,24.5,27.5),10,0.20,27.5,30.5),5,0.10,30.5,33.5),4,0.08,50,1.00,频率,频数,频数、频率的容量的关系,频率的取值范围,频率分布,频率分布表,总体分布,总体分布的估算,(,表,),总体分布的估算,与样本容量的关系,课堂小结,谢谢专家亲临指教,