《统计学基础(英文版·第7版)》教学课件les7e--02-03.pptx
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1、1Copyright 2019,2015,2012,Pearson Education,Inc.ChapterDescriptive Statistics22Copyright 2019,2015,2012,Pearson Education,Inc.Chapter Outline 2.1 Frequency Distributions and Their Graphs 2.2 More Graphs and Displays 2.3 Measures of Central Tendency 2.4 Measures of Variation 2.5 Measures of Position3
2、Copyright 2019,2015,2012,Pearson Education,Inc.Section 2.3Measures of Central Tendency.4Copyright 2019,2015,2012,Pearson Education,Inc.Section 2.3 Objectives How to find the mean,median,and mode of a population and of a sample How to find the weighted mean of a data set,and how to estimate the sampl
3、e mean of grouped data How to describe the shape of a distribution as symmetric,uniform,or skewed and how to compare the mean and median for each.5Copyright 2019,2015,2012,Pearson Education,Inc.Measures of Central TendencyMeasure of central tendency A value that represents a typical,or central,entry
4、 of a data set.Most common measures of central tendency:Mean Median Mode.6Copyright 2019,2015,2012,Pearson Education,Inc.Measure of Central Tendency:MeanMean(average)The sum of all the data entries divided by the number of entries.Sigma notation:x=add all of the data entries(x)in the data set.Popula
5、tion mean:Sample mean:xNxxn.7Copyright 2019,2015,2012,Pearson Education,Inc.Example:Finding a Sample MeanThe weights(in pounds)for a sample of adults before starting a weight-loss study are listed.What is the mean weight of the adults?274 235 223 268 290 285 235.8Copyright 2019,2015,2012,Pearson Edu
6、cation,Inc.Solution:Finding a Sample Mean The sum of the weights isx=274+235+223+268+290+285+235=1810 To find the mean weight,divide the sum of the weights by the number of adults in the sample.The mean weight of the adults is about 258.6 pounds.274 235 223 268 290 285 2359Copyright 2019,2015,2012,P
7、earson Education,Inc.Measure of Central Tendency:MedianMedian The value that lies in the middle of the data when the data set is ordered.Measures the center of an ordered data set by dividing it into two equal parts.If the data set has an odd number of entries:median is the middle data entry.even nu
8、mber of entries:median is the mean of the two middle data entries.10Copyright 2019,2015,2012,Pearson Education,Inc.Example:Finding the MedianFind the median of the weight listed in the first example.274 235 223 268 290 285 235.11Copyright 2019,2015,2012,Pearson Education,Inc.Solution:Finding the Med
9、ian First,order the data.223 235 235 268 274 285 290 There are seven entries(an odd number),the median is the middle,or fourth,data entry.The median weight of the adults is 268 pounds.12Copyright 2019,2015,2012,Pearson Education,Inc.Example:Finding the MedianIn the previous example,the adult weighin
10、g 285 pounds decides to not participate in the study.What is the median weight of the remaining adults?223 235 235 268 274 290.13Copyright 2019,2015,2012,Pearson Education,Inc.Solution:Finding the Median First order the data.223 235 235 268 274 290 There are six entries(an even number),the median is
11、 the mean of the two middle entries.The median weight of the remaining adults is 251.5 pounds.14Copyright 2019,2015,2012,Pearson Education,Inc.Measure of Central Tendency:ModeMode The data entry that occurs with the greatest frequency.If no entry is repeated the data set has no mode.If two entries o
12、ccur with the same greatest frequency,each entry is a mode(bimodal).15Copyright 2019,2015,2012,Pearson Education,Inc.Example:Finding the ModeFind the mode of the weights listed in Example 1.223 235 235 268 274 285 290.16Copyright 2019,2015,2012,Pearson Education,Inc.Solution:Finding the Mode Orderin
13、g the data helps to find the mode.223 235 235 268 274 285 290 The entry of 235 occurs twice,whereas the other data entries occur only once.The mode of the weights is 235 pounds.17Copyright 2019,2015,2012,Pearson Education,Inc.Example:Finding the ModeAt a political debate a sample of audience members
14、 was asked to name the political party to which they belong.Their responses are shown in the table.What is the mode of the responses?Political PartyFrequency,fDemocrat46Republican34Independent39Other/dont know5.18Copyright 2019,2015,2012,Pearson Education,Inc.Political PartyFrequency,fDemocrat46Repu
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