VCU STAT 210 - Lecture12(1) (56 pages)

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Lecture12(1)



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Lecture12(1)

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Pages:
56
School:
Virginia Commonwealth University
Course:
Stat 210 - Basic Practice of Statistics
Basic Practice of Statistics Documents
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STAT 210 Lecture 12 Boxplots September 22 2017 Test 2 Monday September 25 Sections III IV pages 47 95 Combination of multiple choice questions and problems Bring a calculator and writing instrument Practice Problems Pages 94 through 97 Relevant problems IV 7 through IV 12 Recommended problems IV 7 IV 8 and IV 11 Additional Reading and Examples Pages 90 through 93 Motivating Example A 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 13 Top Hat 2 Measures of Central Location 1 Mean influenced by outliers Population mean denoted by m Sample mean denoted by X 2 Median resistant to outliers Population median denoted by h Sample median denoted by M Measures of Spread 1 Range measure of overall spread influenced by outliers 2 Standard Deviation measure of spread around the mean influenced by outliers population standard deviation denoted s sample standard deviation denoted s 3 Interquartile Range measure of spread around the median resistant to outliers Boxplots A 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 and variability spread in a distribution and on the concentration of scores in tails of distribution outliers Boxplots 1 Order the data from smallest to largest Boxplots 1 Order the data from smallest to largest 2 Compute a five number summary Minimum Q1 Median Q3 Maximum Boxplots 1 Order the data from smallest to largest 2 Five number summary Minimum Q1 Median Q3 Maximum 3 Interquartile Range IQR Q3 Q1 Boxplots 1 Order the data from smallest to largest 2 Five number summary Minimum Q1 Median Q3 Maximum 3 Interquartile Range IQR Q3 Q1 4 Lower fence Q1 1 5 IQR Upper fence Q3 1 5 IQR Boxplots 1 2 3 4 Order the data from smallest to largest Five number summary Interquartile Range IQR Q3 Q1 Lower fence Q1 1 5 IQR Upper fence Q3 1 5 IQR Any observation less than the lower fence value or greater than the upper fence value is an outlier Boxplots 1 2 3 4 Order the data from smallest to largest Five number summary Interquartile Range IQR Q3 Q1 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 Boxplots 1 2 3 4 Order the data from smallest to largest Five number summary Interquartile Range IQR Q3 Q1 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 6 Draw boxplot Boxplots i Draw and label an axis 0 10 20 30 Score 40 50 60 70 80 90 100 Boxplots i Draw and label an axis ii Construct a box where the ends of the box are Q1 and Q3 Example suppose Q1 40 and Q3 63 Q1 0 10 20 30 Score 40 Q3 50 60 70 80 90 100 Boxplots i Draw and label an axis ii Construct a box where the ends of the box are Q 1 and Q3 iii Draw a line through the box corresponding to the median Example suppose median 56 Q1 0 10 20 30 Score 40 M 50 Q3 60 70 80 90 100 Boxplots i Draw and label an axis ii Construct a box where the ends of the box are Q 1 and Q3 iii Draw a line through the box corresponding to the median iv Mark an x at the lower and upper adjacent values and draw a dashed line from each x to the end of the box Example suppose lower adjacent value 21 and upper adjacent value 78 Q1 M Q3 x 0 10 20 x 30 Score 40 50 60 70 80 90 100 Boxplots i Draw and label an axis ii Construct a box where the ends of the box are Q 1 and Q3 iii Draw a line through the box corresponding to the median iv Mark an x at the lower and upper adjacent values and draw a dashed line from each x to the end of the box v Indicate all outliers with a circle 0 Q1 x 10 20 30 Score 40 M 50 Q3 60 70 x 80 90 100 0 Q1 x 10 20 30 Score 40 M 50 Q3 60 70 x 80 90 100 Boxplots Location of center median Boxplots Location of center median Measure of spread interquartile range or range Boxplots Location of center median Measure of spread interquartile range or range Shape symmetry or skewness Boxplots Location of center median Measure of spread interquartile range or range Shape symmetry or skewness Existence of outliers Top Hat Example 22 Example 22 1 Data ordered in supplement 2 n 50 n 1 2 50 1 2 25 5 Median 560 560 2 560 There are 25 observations less than 560 Q1 is the median of these 25 observations So Q1 530 There are 25 observations greater than 560 Q3 is the median of these 25 observations So Q3 580 Five number summary 350 530 560 580 720 Example 22 3 IQR Q3 Q1 580 530 50 Example 22 3 IQR Q3 Q1 580 530 50 4 Lower fence Q1 1 5 IQR 530 1 5 50 455 Upper fence Q3 1 5 IQR 580 1 5 50 655 Example 22 4 Lower fence Q1 1 5 IQR 530 1 5 50 455 Upper fence Q3 1 5 IQR 580 1 5 50 655 Outliers Values less than 455 Values greater than 655 Example 22 4 Lower fence Q1 1 5 IQR 530 1 5 50 455 Upper fence Q3 1 5 IQR 580 1 5 50 655 Outliers Values less than 455 350 450 Values greater than 655 Example 22 4 Lower fence Q1 1 5 IQR 530 1 5 50 455 Upper fence Q3 1 5 IQR 580 1 5 50 655 Outliers Values less than 455 350 450 Values greater than 655 720 Example 22 5 Lower adjacent value smallest remaining observation after removing the outliers Example 22 5 Lower adjacent value smallest remaining observation after removing the outliers 470 Example 22 …


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