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1Chapter 3Chapter 3Data DescriptionData Description2OutlineOutlinecircle5Introductioncircle5Measures of Central Tendencycircle5Measures of Variationcircle5Measures of Position3ObjectivesObjectivescircle5Summarize data using the measures of central tendency, such as the mean, median, mode.circle5Describe data using the measures of variation, such as the range, standard deviation andcoefficient of variation.circle5Identify the position of a data value in a data set using various measures of position, such as percentiles, quartiles andz-scores4Measures of Central TendencyMeasures of Central Tendencycircle5Astatisticstatisticis a characteristic or measure obtained by using the data values from a samplecircle5Aparameterparameteris a characteristic or measure obtained by using the data values from a specific population
5The Mean (arithmetic average)circle5Themeanmeanis defined to be the sum of the data values divided by the total number of valuescircle5The mean, in most cases, is not an actual data value circle5We will compute two means: one for the sample and one for a finite population of values6The Sample MeanThe Sample MeannXnXXXXn∑=+++...=21XThe symbol represents the sample mean.is read as “X-bar”.The Greek symbol is read as “sigma”and it means “to sum”XThe Sample Mean The Sample Mean -ExampleExampleweeksnXXThe ages in weeks of a random sample of six kittens at an animal shelter are 3, 8, 5, 12,14 and 12Find the average age of this sampleThe Population MeanThe Population Mean8
93-121220,000$=59,000+9,000+12,000+20,000+50,000==NX∑μA small company consists of the owner, the manager, the salesperson, and two technicians. The salaries are listed as $50,000, $20,000, $12,000, $9,000 and $9,000 respectively (Assume this is the population)Then the population mean will be:10MDMDThe Median The Median -Example Example circle5The weights (in pounds) of seven soldiers are 180, 201, 220, 191, 219, 209, and 186. Find the mediancircle5Arrange the data in order and select the middle pointThe Population Mean-Example Example -The Median The Median circle5When a data set is ordered, it is called adata arraydata arraycircle5Themedianmedianis defined to be the midpoint of the data arraycircle5The symbol used to denote the median is12
13The Median The Median circle5In the previous example, there was an odd numberodd numberof values in the data setcircle5In this case it is easy to select the middle number in the data array14The Median The Median circle5When there is aneven numbereven numberof values in the data set, the median is obtained by taking theaverage average of the two middle numbersof the two middle numbers