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1、统计学基础(英文版第7版)教学课件les7e_ppt_02_03,统计学基础(英文版第7版)教学课件les7e_ppt_,Chapter Outline,2.1 Frequency Distributions and Their Graphs2.2 More Graphs and Displays2.3 Measures of Central Tendency2.4 Measures of Variation2.5 Measures of Position,Chapter Outline2.1 Frequency D,Section 2.3,Measures of Central Tenden
2、cy,.,Section 2.3Measures of Central,Section 2.3 Objectives,How to find the mean, median, and mode of a population and of a sampleHow to find the weighted mean of a data set, and how to estimate the sample mean of grouped dataHow to describe the shape of a distribution as symmetric, uniform, or skewe
3、d and how to compare the mean and median for each,.,Section 2.3 ObjectivesHow to f,Measures of Central Tendency,Measure of central tendencyA value that represents a typical, or central, entry of a data set.Most common measures of central tendency:MeanMedianMode,.,Measures of Central TendencyMe,Measu
4、re of Central Tendency: Mean,Mean (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.Population mean:Sample mean:,.,Measure of Central Tendency: M,Example: Finding a Sample Mean,The weights (in pounds) for a s
5、ample 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,.,Example: Finding a Sample Mean,Solution: Finding a Sample Mean,The sum of the weights isx = 274 + 235 + 223 + 268 + 290 + 285 + 235 = 1810To find the mean weight, divid
6、e the sum of the weights by the number of adults in the sample.,The mean weight of the adults is about 258.6 pounds.,.,274 235 223 268 290 285 235,Solution: Finding a Sample Mea,Measure of Central Tendency: Median,MedianThe value that lies in the middle of the data when the data set is ordered.Measu
7、res the center of an ordered data set by dividing it into two equal parts.If the data set has anodd number of entries: median is the middle data entry.even number of entries: median is the mean of the two middle data entries.,.,Measure of Central Tendency: M,Example: Finding the Median,Find the medi
8、an of the weight listed in the first example. 274 235 223 268 290 285 235,.,Example: Finding the MedianFin,Solution: Finding the Median,First, order the data.223 235 235 268 274 285 290There are seven entries (an odd number), the median is the middle, or fourth, data entry.,The median weight of the
9、adults is 268 pounds.,.,Solution: Finding the MedianFi,Example: Finding the Median,In the previous example, the adult weighing 285 pounds decides to not participate in the study. What is the median weight of the remaining adults?223 235 235 268 274 290,.,Example: Finding the MedianIn,Solution: Findi
10、ng the Median,First order the data.223 235 235 268 274 290There are six entries (an even number), the median is the mean of the two middle entries.,The median weight of the remaining adults is 251.5 pounds.,.,Solution: Finding the MedianFi,Measure of Central Tendency: Mode,ModeThe data entry that oc
11、curs with the greatest frequency.If no entry is repeated the data set has no mode.If two entries occur with the same greatest frequency, each entry is a mode (bimodal).,.,Measure of Central Tendency: M,Example: Finding the Mode,Find the mode of the weights listed in Example 1.223 235 235 268 274 285
12、 290,.,Example: Finding the ModeFind,Solution: Finding the Mode,Ordering the data helps to find the mode.223 235 235 268 274 285 290The entry of 235 occurs twice, whereas the other data entries occur only once.,The mode of the weights is 235 pounds.,.,Solution: Finding the ModeOrde,Example: Finding
13、the Mode,At a political debate a sample of audience members 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?,.,Example: Finding the ModeAt a,Solution: Finding the Mode,The response occurring with the greatest frequ
14、ency is Democrat. So, the mode is Democrat. In this sample, there were more Democrats than people of any other single affiliation.,.,Political PartyFrequency, fDem,Comparing the Mean, Median, and Mode,All three measures describe a typical entry of a data set.Advantage of using the mean:The mean is a
15、 reliable measure because it takes into account every entry of a data set.Disadvantage of using the mean:Greatly affected by outliers (a data entry that is far removed from the other entries in the data set).,.,Comparing the Mean, Median, an,Example: Comparing the Mean, Median, and Mode,The table sh
16、ows the sample ages of students in a class. Find the mean, median, and mode of the ages. Are there any outliers? Which measure of central tendency best describes a typical entry of this data set?,.,Example: Comparing the Mean, M,Solution: Comparing the Mean, Median, and Mode,Mean:,Median:,20 years (
17、the entry occurring with thegreatest frequency),Mode:,.,Solution: Comparing the Mean,Solution: Comparing the Mean, Median, and Mode,Mean 23.8 years Median = 21.5 years Mode = 20 years,The mean takes every entry into account, but is influenced by the outlier of 65. The median also takes every entry i
18、nto account, and it is not affected by the outlier.In this case the mode exists, but it doesnt appear to represent a typical entry.,.,Solution: Comparing the Mean,Solution: Comparing the Mean, Median, and Mode,Sometimes a graphical comparison can help you decide which measure of central tendency bes
19、t represents a data set.,In this case, it appears that the median best describes the data set.,.,Solution: Comparing the Mean,Weighted Mean,Weighted MeanThe mean of a data set whose entries have varying weights.The weighted mean is given by where w is the weight of each entry x.,.,Weighted MeanWeigh
20、ted Mean.,Example: Finding a Weighted Mean,Your grades from last semester are in the table. The grading system assigns points as follows: A = 4, B = 3, C = 2, D = 1, F = 0. Determine your grade point average (weighted mean).,.,Example: Finding a Weighted Me,Solution: Finding a Weighted Mean,Last sem
21、ester, your grade point average was 2.5.,.,Solution: Finding a Weighted M,Mean of Grouped Data,Mean of a Frequency DistributionApproximated by where x and f are the midpoints and frequencies of a class, respectively.,.,Mean of Grouped DataMean of a,Finding the Mean of a Frequency Distribution,In Wor
22、ds In Symbols,Find the midpoint of each class.Find the sum of the products of the midpoints and the frequencies.Find the sum of the frequencies.Find the mean of the frequency distribution.,.,Finding the Mean of a Frequenc,Example: Find the Mean of a Frequency Distribution,The frequency distribution
23、shows the out-of-pocket prescription medicine expenses (in dollars) for 30 U.S. adults in a recent year. Use the frequency distribution to estimate the mean expense. Using the sample mean formula, the mean expense is $285.50. Compare this with the estimated mean.,.,Example: Find the Mean of a Fr,Sol
24、ution: Find the Mean of a Frequency Distribution,.,The mean expense is $287.70. This value is an estimate because it is based on class midpoints instead of the original data set.,Solution: Find the Mean of a F,The Shape of Distributions,Symmetric DistributionA vertical line can be drawn through the
25、middle of a graph of the distribution and the resulting halves are approximately mirror images.,.,The Shape of DistributionsSymm,The Shape of Distributions,Uniform Distribution (rectangular)All entries or classes in the distribution have equal or approximately equal frequencies.Symmetric.,.,The Shap
26、e of DistributionsUnif,The Shape of Distributions,Skewed Left Distribution (negatively skewed)The “tail” of the graph elongates more to the left.The mean is to the left of the median.,.,The Shape of DistributionsSkew,The Shape of Distributions,Skewed Right Distribution (positively skewed)The “tail” of the graph elongates more to the right.The mean is to the right of the median.,.,The Shape of DistributionsSkew,感谢聆听,感谢聆听,
