CHAPTER 3 Data DescriptionStat 200 – Elementary StatisticsIntroductionSection 3.1 Measures of Central TendencyExample: Weight of wild bearsSection 3.2 Measures of VariationExample: Find the mean of each groupCoefficient of VariationEmpirical Rule for Normal DistributionsInterpreting Z ScoresPercentiles, Quartiles, and DecilesExampleBoxplots and Five-Number SummariesExampleStat 200 – Elementary Statistics Introduction Section 3.1 Measures of Central TendencyStatisticParameterData ArrayMeanWeighted MeanSummationVariables XExample: The data represent the annual chocolate sales (in billionsof dollars) for a sample of seven countries in the world. Find the mean.2.0, 4.9, 6.5, 2.1, 5.1, 3.2, 16.6Student NotesCHAPTER 3 Data DescriptionExample: Weight of wild bears Weight Frequency Midpoints f·Xm0 - 49 6 24.550 - 99 10 74.5100 - 149 10 124.5150 - 199 7 174.5200 - 249 8 224.5250 - 299 2 274.5300 - 349 4 324.5350 - 399 3 374.5400 - 449 3 424.5450 - 499 0 474.5500 - 549 1 524.5Weighted MeanExample: Find the student’s grade point average if he received the following grades:Composition I 3 A(4 points)Intro. to Psychology 3 C(2 points)Biology 4 B(3 points)Physical Ed. 2 D(1 pointMedianModeModal ClassExample: Find the median for the data.34, 23, 33, 36, 48, 34,26, 45, 29X-nXfXmFind the median for the data.34, 23, 33, 36, 48, 34,26, 45Example: Find the mode for the data.34, 23, 33, 36, 48, 34,26, 45, 29Example: The annual salaries for different positions are listed. Find the mean, median, and mode for the data.Staff SalaryOwner $50,000Manager $20.000Salesperson $12,000Technician $9,000Technician $9,000MidrangeDistribution ShapesSection 3.2 Measures of VariationExample: Find the mean of each group Group A Group B10 3560 4550 3030 3540 4020 25RangePopulation Variance and Standard DeviationExample: Find the variance and standard deviation for the data set for Group A 10, 60, 50, 30, 40, 20Find the variance and standard deviation for the data set for Group B35, 45, 30, 35, 40, 25Sample Variance and Standard DeviationFind the variance and standard deviation for the data set11.2, 11.9, 12.0, 12.8, 13.4, 14.32s2ssVariance and Standard Deviation for Grouped DataCoefficient of VariationRule of ThumbChebyshev’s TheoremThe proportion of values from a data set that will fall within k standard deviations of the mean will be at least 1 – 1/k2; where k is a number greater than 1. Empirical Rule for Normal Distributions)1(])[(222-- nnXfXfnsmm3.4 Measures of Positionz scoreA student scored 65 on a calculus test that had a mean of 50 and a standard deviation of 10; she scored 30 on a history test with a mean of 25 and a standard deviation of 5. Compare her relative positions on the two tests.Interpreting Z ScoresExampleCompare Joe’s height of 78 in. to Susan’s height of 76 in. Use the following information: Men have heights with a mean of 69.0 in. and st. dev. of 2.8 in.; women have heights with mean of 63.6 in. and a st. dev. of 2.5 in.Percentiles, Quartiles, and DecilesPercentile FormulaExampleA teacher gives a 20-point test to 10 students. The scores are shown below. Find the percentile rank of a score of 12.18, 15, 12, 6, 8, 2, 3, 5, 20, 10ExampleFind the value corresponding to the 25th percentile.18, 15, 12, 6, 8, 2, 3, 5, 20, 10Finding Data Values Corresponding to Q1,Q2, and Q3Step 1Step 2Step 3Step 4ExampleFind Q1,Q2, and Q3 for the data set 15, 13, 6, 5, 12, 50, 22, 18OutliersExampleCheck the following data set for outliers. 5, 6, 12, 13, 15, 18, 22, 503.4 Exploratory Data AnalysisBoxplots and Five-Number SummariesExampleFind 5-number summary and construct a boxplot.32 37 36 32 51 53 33 61 35 45 5539 76 37 42 40 32 60 38 56 48 4840 43 62 43 42 44 41 56 39 46 3147 45 60 46 40