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- 1. Measures of Variation. . 8 12 16 20 24 28 32 36 40 44 48 52 56 60 Measures of Variation Box and Whisker
- 2. Median • The middle number in a data set when the data are ordered from least to greatest. 3, 4, 4, 5, 6, 7, 8 3, 4, 4, 5, 6, 7, 8, 9 5 + 6 = 11 11 2 = 5.5 Odd Number of Data Even Number of Data
- 3. Measures of Variation • Measures of variation are used to describe the distribution of the data. Upper and Lower Quartiles The upper and lower quartiles are the medians of the upper half and lower half of a set of data, respectively. Interquartile Range The range of the middle half of the data. It is the difference between the upper quartile and the lower quartile. Range The difference between the greatest and least data values 20, 22, 22, 25, 27, 30, 31, 35 median Upper quartileLower quartile 30 + 31 = 6122 + 22 = 44 44 2 = 22 61 2 = 30.5 30.5 – 22 = 8.5 35 – 20 = 15 Lower quartile = 22 Upper quartile = 30.5 median 25 + 27 = 52 52 2 = 26
- 4. 4, 4, 6, 7, 8, 10, 12, 15, 19 Measures of Variation medianLower quartile Upper quartile Interquartile range 85 13.5 8.5 Range 15 13.5 - 5 19 - 4
- 5. 4, 4, 6, 7, 8, 10, 12, 19 Measures of Variation medianLower quartile Upper quartile Interquartile range 7.55 11 6 Range 15
- 6. Outlier• An outlier is a data value that is either much greater or much less than the median. If a data value is more than 1.5 times the value of the interquartile range beyond the quartiles, is an outlier. 2, 21, 23, 23, 24, 25, 27, 31 Lower quartile Upper quartile Interquartile range 4 X 1.5 6 22 26 4 Add 6Subtract 6 26 + 6 = 3222 – 6 = 16 If 31 is greater than or equal to 32. It is an outlier. If 2 is less than or equal to 16. It is an outlier Outlier Test Outlier Test Pass Fail
- 7. 4, 4, 6, 7, 8, 10, 12, 19 Outlier Test medianLower quartile Upper quartile Interquartile range 7.55 11 6 6 X 1.5 9 9 + 11 = 205 – 9 = -4 Outlier TestOutlier Test
- 8. -7, 3, 5, 6, 8, 9, 11, 25 Outlier Test medianLower quartile Upper quartile Interquartile range 7 10 6 6 X 1.5 9 10 + 9 = 194 – 9 = -5 Outlier TestOutlier Test 4
- 9. -3, 4, 6, 7, 8, 9, 17, 24 Outlier Test medianLower quartile Upper quartile Interquartile range 7.5 13 8 8 X 1.5 12 Outlier TestOutlier Test 5 5 – 12 = -7 13 + 12 = 25
- 10. -3, -2, 4, 5, 5, 12, 18, 30 Outlier Test medianLower quartile Upper quartile Interquartile range 5 15 14 14 X 1.5 21 Outlier TestOutlier Test 1 1 – 21 = -20 15 + 21 = 36
- 11. Box-and-Whisker Plots 8 12 16 20 24 28 32 36 40 44 48 52 56 60 • A box-and-whisker plot is a diagram that is constructed using the median, quartiles, and extreme values. A box is drawn around the quartile values, and the whiskers extend from each quartile to the extreme values. The median is marked with a vertical line. .. . Upper quartileLower quartile median Interquartile range 42 – 30 = 12 Upper extremeLower extreme The outlier will be shown with a small symbol that is off the Box-and-Whisker Plot
- 12. Box-and-Whisker Plots 8 12 16 20 24 28 32 36 40 44 48 52 56 60 .. . Upper quartileLower quartile median Interquartile range 31 - 22 = 9 8, 20, 22, 22, 25, 27, 30, 31, 35, 52 median Upper quartileLower quartile 26 Lower extreme Upper extreme OutlierOutlier
- 13. Box-and-Whisker Plots 8 12 16 20 24 28 32 36 40 44 48 52 56 60 .. . Upper quartileLower quartile median Interquartile range 32 - 20 = 12 8, 19, 20, 20, 21 22, 26, 27, 30, 34, 35, 44 median Upper quartileLower quartile Lower extreme Upper extreme
- 14. Box-and-Whisker Plots 8 12 16 20 24 28 32 36 40 44 48 52 56 60 .. . Upper quartileLower quartile median Interquartile range 32 - 20 = 12 6, 16, 20, 20, 21 22, 26, 27, 30, 34, 35, 44 median Upper quartileLower quartile Lower extreme Upper extreme Outlier
- 15. Box-and-Whisker Plots 8 12 16 20 24 28 32 36 40 44 48 52 56 60 .. . Upper quartileLower quartile median 12, 13, 15, 17, 21 26, 26, 27, 27, 29, 35, 38 median Upper quartileLower quartile Lower extreme Upper extreme
- 16. Box-and-Whisker Plots 8 12 16 20 24 28 32 36 40 44 48 52 56 60 .. median 8, 9, 16, 18, 30 32, 36, 40, 44, 46, 50, 58 median Upper quartileLower quartile Upper extreme Lower quartile Upper quartile . Lower extreme
- 17. Box-and-Whisker Plots 8 12 16 20 24 28 32 36 40 44 48 52 56 60 .. . 16, 20, 21, 23, 28 29, 35, 37, 37, 49, 55, 57 median Upper quartileLower quartile
- 18. Box-and-Whisker Plots 8 12 16 20 24 28 32 36 40 44 48 52 56 60 .. . Median_______________ Upper quartile_________ Lower quartile_________ Upper extreme________ Lower extreme________ Outlier_______________ 30 40 24 50 16 no outlier
- 19. Box-and-Whisker Plots 8 12 16 20 24 28 32 36 40 44 48 52 56 60 .. . Median_______________ Upper quartile_________ Lower quartile_________ Upper extreme________ Lower extreme________ Outlier_______________ 42 50 32 60 26 8
- 20. Box-and-Whisker Plots 8 12 16 20 24 28 32 36 40 44 48 52 56 60 .. . Median_______________ Upper quartile_________ Lower quartile_________ Upper extreme________ Lower extreme________ Outlier_______________ 36 44 32 52 28 10
- 21. Box-and-Whisker Plots 8 12 16 20 24 28 32 36 40 44 48 52 56 60 .. . Median_______________ Upper quartile_________ Lower quartile_________ Upper extreme________ Lower extreme________ Outlier_______________ 18 26 32 8 60 13

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