Slide 1Test 2Practice ProblemsAdditional Reading and ExamplesSlide 5Motivating ExampleMotivating ExampleMotivating ExampleMotivating ExampleMotivating ExampleGoalStatisticsNotationMeasures of Central LocationMeasures of Central LocationMeasures of Central LocationExample 13Example 13Measures of Central LocationExample 14Example 14Example 14Slide 23Measures of Central LocationMeasures of Central LocationMedianMedianMedianMedianMedianExample 15Example 15Example 15Example 16Example 16Example 16Example 16DistributionsSymmetricDistributionsSkewed RightSkewed LeftSlide 43TI-83/84 CalculatorMotivating ExampleMotivating Example SolutionSTAT 210Lecture 10Measures of CenterSeptember 18, 2017Test 2Monday, September 25Sections III - IV (pages 47 - 95)Combination of multiple choice questions and short answer questions and problems.Bring a calculator and writing instrument.Practice ProblemsPages 94 through 97Relevant problems: IV.1, IV.2, IV.3,IV.5, IV.6 (a) and (b), and IV.11 (c) Recommended problems: IV,1, IV.2 and IV.6 (a) and (b)Additional Reading and ExamplesPages 90 through 93Top HatMotivating ExampleA statistics course at a large university provides free to students statistics review sessions that students can use to answer questions, with help solving problems, and with help studying for tests. The course instructor is interested in the number of students who attend each hour of review session, and selects a sample of 15 review session hours spread out over a month’s time. As described, what is the population of interest for this example?Motivating ExampleA statistics course at a large university provides free to students statistics review sessions that students can use to answer questions, with help solving problems, and with help studying for tests. The course instructor is interested in the number of students who attend each hour of review session, and selects a sample of 15 review session hours spread out over a month’s time. As described, what is the population of interest for this example?Answer: one could say all students currently taking statistics, but the data in the sample is collected on the review sessions, so the population of interest would be all review sessions held for this statistics course.Motivating ExampleA statistics course at a large university provides free to students statistics review sessions that students can use to answer questions, with help solving problems, and with help studying for tests. The course instructor is interested in the number of students who attend each hour of review session, and selects a sample of 15 review session hours spread out over a month’s time. As described, what is the population of interest for this example?What type of characteristic is the number of students who attend each hour of review session?Motivating ExampleA statistics course at a large university provides free to students statistics review sessions that students can use to answer questions, with help solving problems, and with help studying for tests. The course instructor is interested in the number of students who attend each hour of review session, and selects a sample of 15 review session hours spread out over a month’s time. As described, what is the population of interest for this example?What type of characteristic is the number of students who attend each hour of review session?Answer: number of students attending a review session is countable and hence is a discrete quantitative variable.Motivating ExampleA statistics course at a large university provides free to students statistics review sessions that students can use to answer questions, with help solving problems, and with help studying for tests. The course instructor is interested in the number of students who attend each hour of review session, and selects a sample of 15 review session hours spread out over a month’s time. The number of students who attended these 15 review session hours is as follows. This data will be used throughout the rest of this chapter.6 1 8 3 1 5 11 7 4 28 12 9 2 10 13GoalDetermine the value of a population parameter, designatedusing Greek letters (such as m, s and p).1. Central location parameter - locate the center of the distribution2. Dispersion parameter - measure the spread or variability around the centerStatisticsAll subjects of the population are rarely known. Hence the population parameter of interest can rarely be determined and must be estimated using a sample statistic. The statistics are denoted using regular letters, such as X, s and p.Such an estimation is a type of statistical inference.Notationn = number of observations in the samplex1 = value of first observationx2 = value of second observation...xn = value of nth (last) observationMeasures of Central Location1. Mean (Average)The mean is the most often used measure of central location, including being used in many of the inference procedures we will discuss later in the course.Measures of Central Location1. Mean (Average)The population mean is denoted by the Greek letter m (read “mu”) and is the sum of all observations divided by how many individuals that there are in the population. This is (usually) an unknown parameter.Measures of Central LocationThe population mean is estimated by the sample mean, denoted by X (read “X-bar”).X = S x = x1 + x2 + x3 + … + xn n nThe sample mean X is a statistic.The symbol S implies to “sum” or “add” what follows.Example 13In this example are we calculating the population mean m or the sample mean X?Example 13X = S x = 128+150+183+222+113+154+201+150 n 8 = 1301/8 = 162.625 poundsMeasures of Central LocationThe mean is highly influenced by outliers (extreme values).Example 14Example 14X = S x = 128+150+183+222+113+154+201+150+391 n 9 = 1692 / 9 = 188 poundsExample 14X = S x = 128+150+183+222+113+154+201+150+391 n 9 = 1692 / 9 = 188 poundsHence the outlier value of 391 pounds has increased the sample mean from 162.625 to 188 pounds (a 25.375 pound increase).Top HatMeasures of Central Location2. MedianThe median is more resistant to outliers than the mean, and is the central value with half of the observations less than it and half of the observations greater than it.Measures of Central Location2. MedianThe population median is usually denoted by the Greek letter h (read “eta”), and is estimated by the
View Full Document
Unlocking...