总体分布估计.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,*,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,*,10.6,总体分布估计,第十章 概率统计,1,1.,会列频率分布表,2.,会画频率分布直方图,学习目标：,2,当使用了随机抽样完成样本数据的收集之后，就需要利用样本数据估计总体分布情况，就需要把收集到的数据分布情况整理出来。,今天给大家介绍两种对数据进行加工整理的基本方法：,列频率分布表、画频率分布直方图,3,探究,1,月,2,月,3,月,4,月,5,月,6,月,7,月,8,月,9,月,10,月,11,月,12,月,西安,9.2,4.9,5.4,18.6,38.0,106.3,54.4,128.9,62.9,73.6,26.2,10.6,桂林,41.4,53.3,178.8,273.5,384.9,432.4,67.5,228.5,201.4,147.3,28.0,19.1,下表给出,2000,年西安和桂林各月的降水量（单位：,mm,）,填写下表,，,试分析两地一年中降水量偏大（大于,100mm,）的状况,总月数,降水量偏大月数（频数）,频率,西安,桂林,12,12,2,7,0.17,0.58,1,、列频率分布表,4,例,1,、一位植物学家想要研究某种植物生长一年之后的高度，他随机抽取了,60,棵此种植物，测得它们生长一年后的高度如下（单位：,cm,）：,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 99 76 72,72 91 86 75 76 50 69 69 56 74,试列出该样本的频率分布表,5,制作频率分布表的一般步骤,第一步：计算极差，即计算一组数据的最大值与最小值的差，又称全距。,最大值,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 99 76 72,72 91 86 75 76 50 69 69 56 74,最小值,99-41=58,第二步：决定组距（即分成的区间的长度）和组数。,样本有,60,个数据，可将样本分成,8,12,组，本例若分成,10,组，则,取整数，组距可定为,6cm,6,第三步：确定各组分点。,确定各组分点的原则是既要把全部数据包括在内，又要使每一个在一个确定的组内。,一般取比数据多一位小数，且把第一组起点减小一点。,第一组的起点定为,40.5,，组距为,6,，这样所分的,10,个组是：,40.5,46.5,，,46.5,52.5,，,52.5,58.5,，,58.5,64.5,，,64.5,70.5,，,70.5,76.5,，,76.5,82.5,，,82.5,88.5,，,88.5,84.5,，,94.5,100.5,7,第四步：列频率分布表。,高度分组,频数,频率,40.5,46.5,46.5,52.5,52.5,58.5,58.5,64.5,64.5,70.5,70.5,76.5,76.5,82.5,82.5,88.5,88.5,94.5,94.5,100.5,合计,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 99 76 72,72 91 86 75 76 50 69 69 56 74,4,5,6,12,13,6,5,5,1,3,60,0.067,0.050,0.083,0.100,0.200,0.217,0.100,0.083,0.053,0.017,1,8,1,、找出数据的最大值和最小值，算出极差,2,、决定组数,数据个数在,50,100,个时，分成,6,10,组，,数据个数在,100,250,个时，分成,7,12,组,3,、决定组距和分点,分点比原数据精确度高一位,4,、计算频数和频率，列出频率分布表,（,1,）频数：每一组数据的个数叫做该组数据的频数,（,2,）频率：频数,/,数据总个数,制作频率分布表的一般步骤,9,学生练习：,P 179,10,为了更直观地体现数据的分布规律，我们可以利用直方图反映样本的频率分布规律，这样的直方图称为频率分布直方图,。,2,、,频率分布直方图,11,例,2,、作出例,1,中数据的频率分布直方图,（,1,）制作频率分布表，作直角坐标系，横坐标表示高度，纵坐标表示,（,2,）在横坐标上标上,40.5,，,46.5,，,52.5,，,，,100.5,40.5,52.5,46.5,64.5,58.5,76.5,70.5,82.5,88.5,94.5,100.5,0.003,0.011,0.016,0.036,（,3,）在坐标系中，分别将横坐标上标出的相邻两点的线段位底作矩形，高,等与该组的,这样，就得到了这组数据的频率分布直方图,12,1,、,横坐标：分组的数据值,2,、,纵坐标：,该组的频率,/,组距,3,、,每个矩形的面积恰好是该组的频率,作频率分布直方图的方法,13,例,3,、,从某校一年级,1005,名新生中按系统抽样的方法抽取一个容量为,100,的身高样本，数据如下,（单位：,cm,）,168,165,171,167,170,165,170,152,175,174,165,170,168,169,171,166,164,155,164,158,170,155,166,158,155,160,160,164,156,162,160,170,168,164,174,171,165,179,163,172,180,174,173,159,163,172,167,160,164,169,151,168,158,168,176,155,165,165,169,162,177,158,175,165,169,151,163,166,163,167,178,165,158,170,169,159,155,163,153,155,167,163,164,158,168,167,161,162,167,168,161,165,174,156,167,166,162,161,164,166,（,1,）编制频率分布表；,（,2,）绘制频率分布直方图；,（,3,）估计该,该校新生身高低于,160cm,的约占多少，,身高在,174cm,以上的,约占多少,14,（,1,）频率分布表如下,分组,频数,频率,频率,/,组距,150.5,153.5,4,0.04,0.013,153.5,156.5,8,0.08,0.027,156.5,159.5,8,0.08,0.027,159.5,162.5,11,0.11,0.037,162.5,165.5,22,0.22,0.073,165.5,168.5,19,0.19,0.063,168.5,171.5,14,0.14,0.047,171.5,174.5,7,0.07,0.023,174.5,177.5,4,0.04,0.013,177.5,180.5,3,0.03,0.010,合计,100,1,15,（,2,）直方图如图：,0.027,0.037,0.073,16,布置作业：课本习题,小结,1,、,列频率分布表,2,、,画频率分布直方图,17,