Slide 1Practice ProblemsAdditional Reading and ExamplesTest 2Slide 5Motivating ExampleSlide 7Measures of Central LocationB. Measures of SpreadTI-83/84 CalculatorMotivating ExampleMotivating Example SolutionExample - AnswersExample - AnswersExample - AnswersSlide 16BoxplotsBoxplotsBoxplotsBoxplotsBoxplotsBoxplotsBoxplotsBoxplotsBoxplotsSlide 26BoxplotsSlide 28BoxplotsSlide 30BoxplotsSlide 32BoxplotsSlide 34BoxplotsBoxplotsBoxplotsBoxplotsSlide 39Example 22Example 22Example 22Example 22Example 22Example 22Example 22Example 22Example 22Example 22Example 22Example 22Example 22Example 22Example 22BoxplotsBoxplotsBoxplotsExample 22BoxplotsTI-83/84 CalculatorMotivating ExampleMotivating Example SolutionSlide 63STAT 210Lecture 12BoxplotsSeptember 22, 2016Practice ProblemsPages 94 through 97Relevant problems: IV.7 through IV.12Recommended problems: IV.7, IV.8 and IV.11Additional Reading and ExamplesPages 90 through 93Test 2Monday, September 26Questions for the first 10 minutes, then test – papers due promptly at the end of class!Covers chapters 3 and 4 (pages 43 – 97)Combination of multiple choice questions and short answer questions and problems.Formulas provided; Bring a calculator!Practice Tests and Formula Sheet on Blackboard.ClickerMotivating ExampleA statistics course at a large university provides free 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 mean number of students who attend all review sessions held for this statistics course, and selects a sample of 15 review sessions spread out over a month’s time. The number of students who attended these 15 review sessions is as follows. How would you create a boxplot for this data?6 1 8 3 1 5 11 7 4 28 12 9 2 10 13ClickerMeasures of Central Location1. Mean – influenced by outliers - Population mean denoted by m - Sample mean denoted by X2. Median – resistant to outliers - Population median denoted by h - Sample median denoted by MB. Measures of Spread1. Range – measure of overall spread, influenced by outliers2. Standard Deviation – measure of spread around the mean, influenced by outliers- population standard deviation denoted s- sample standard deviation denoted by s 3. Interquartile Range – measure of spread around the median, resistant to outliersTI-83/84 CalculatorSee page 93 for instructions for using a calculator to compute the measures of center and spread.1. Hit STAT, then option 1:Edit, then enter the data into a list.2. Hit STAT, then scroll over to CALC3. Choose option 1: 1-Var Stats4. If the data is not in list 1 (L1), indicate the list the data is in (L2, L3, etc.) and hit ENTER5. X is the sample mean, Sx is the sample standard deviation, use minX and maxX to calculate the range, use Q1 and Q3 to calculate the IQR, and Med is the median.Motivating ExampleA statistics course at a large university provides free 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 mean number of students who attend all review sessions held for this statistics course, and selects a sample of 15 review sessions spread out over a month’s time. The number of students who attended these 15 review sessions is as follows. Calculate the range, standard deviation and IQR for this data.6 1 8 3 1 5 11 7 4 28 12 9 2 10 13Motivating Example Solution1 1 2 3 4 5 6 7 8 9 10 11 12 13 28Range = 28 – 1 = 27Standard deviation = 6.782IQR = Q3 – Q1 = 11 – 3 = 8Example - Answersx x - X (x - X)21 1 – 8 = -7 491 1 – 8 = -7 492 2 – 8 = -6 363 3 – 8 = -5 254 4 – 8 = -4 165 5 – 8 = -3 96 6 – 8 = -2 4 7 7 – 8 = -1 18 8 – 8 = 0 09 9 – 8 = 1 110 10 – 8 = 2 411 11 – 8 = 3 912 12 – 8 = 4 1613 13 – 8 = 5 2528 28 – 8 = 20 400 0 644X = 120/15 = 8Example - Answerss = S (x - X)2 = 644 = 46 = 6.782 n - 1 15 - 1Example - Answers1 1 2 3 4 5 6 7 8 9 10 11 12 13 28n = 15, (n+1)/2 = (15+1)/2 = 16/2 = 8So median is 7.For the quartiles, n = 7, (n+1)/2 = (7+1)/2 = 8/2 = 4Q1 is 3.Q3 is 11.IQR = Q3 – Q1 = 11 – 3 = 8Clicker2BoxplotsA graphical display which uses several of the numerical measures to give information on the symmetry or skewness (shape) of the distribution, on the central location (center) and variability (spread) in a distribution, and on any outliers in the distribution (unusual features).Boxplots1. Order the data from smallest to largest.Boxplots1. Order the data from smallest to largest.2. Compute a five-number summary Minimum Q1 Median Q3 MaximumBoxplots1. Order the data from smallest to largest.2. Five-number summary Minimum Q1 Median Q3 Maximum3. Interquartile Range: IQR = Q3 - Q1Boxplots1. Order the data from smallest to largest.2. Five-number summary Minimum Q1 Median Q3 Maximum3. Interquartile Range: IQR = Q3 - Q14. Lower fence = Q1 - 1.5 IQR Upper fence = Q3 + 1.5 IQRBoxplots1. Order the data from smallest to largest.2. Five-number summary3. Interquartile Range: IQR = Q3 - Q14. Lower fence = Q1 - 1.5 IQR Upper fence = Q3 + 1.5 IQR Outliers: any observation less than the lower fence value or greater than the upper fence value is an outlier.Boxplots1. Order the data from smallest to largest.2. Five-number summary3. Interquartile Range: IQR = Q3 - Q14. Lower fence = Q1 - 1.5 IQR Upper fence = Q3 + 1.5 IQR Outliers: any observation less than the lower fence value or greater than the upper fence value.5. After removing the outliers, the lower adjacent value is the smallest observation that remains in the data set and the upper adjacent value is the largest observation that remains in the data set.Boxplots1. Order the data from smallest to largest.2. Five-number summary3. Interquartile Range: IQR = Q3 - Q14. Lower fence = Q1 - 1.5 IQR Upper fence = Q3 + 1.5 IQR Outliers: any observation less than the lower fence value or greater than the upper fence
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