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Measures of Central Tendency And Variation

Measures of Central Tendency And Variation. Measures of Central Tendency. Mean Average The sum of the numbers divided by the number of numbers Represented by x Median Middle number of the ordered numbers from least to greatest Mean of middle two numbers Mode

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Measures of Central Tendency And Variation

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  1. Measures of Central Tendency And Variation

  2. Measures of Central Tendency • Mean • Average • The sum of the numbers divided by the number of numbers • Represented by x • Median • Middle number of the ordered numbers from least to greatest • Mean of middle two numbers • Mode • The number or numbers that occur most frequently • There may be one mode, no mode, or more than one mode.

  3. Measures of Variation • Range • Difference between the greatest and the least values. • Quartiles • Values that separate the data into four equal subsets, each containing one fourth of the data. • Lower Quartile • It divides the lower half of the data into two equal parts. • Upper Quartile • It divides the upper half of the data into two equal parts. • Interquartile Range (IQR) • Difference between the upper and lower quartiles • Outlier • A value that is much less or much greater than the rest of the data. • Any element of a set of data that is at least 1.5 interquartile ranges less than the lower quartile or greater than the upper quartile.

  4. Measures of Variation 1 1 2 4 6 7 7 8 9 10 12 13 17 17 18

  5. Measures of Variation 1 1 2 4 6 7 7 8 9 10 12 13 17 17 18 median

  6. Measures of Variation 1 1 2 4 6 7 7 8 9 10 12 13 17 17 18 median Lower Quartile (LQ)

  7. Measures of Variation 1 1 2 4 6 7 7 8 9 10 12 13 17 17 18 median Lower Quartile (LQ) Upper Quartile (UQ)

  8. Measures of Variation 1 1 2 4 6 7 7 8 9 10 12 13 17 17 18 median Lower Quartile (LQ) Upper Quartile (UQ) UQ – LQ = IQR

  9. Outlier 1 8 9 10 10 11 12 13 13 15 27

  10. Outlier 1 8 9 10 10 11 12 13 13 15 27 Median

  11. Outlier 1 8 9 10 10 11 12 13 13 15 27 LQ Median

  12. Outlier 1 8 9 10 10 11 12 13 13 15 27 LQ Median UQ

  13. Outlier 1 8 9 10 10 11 12 13 13 15 27 IQR = 13 – 9 = 4 LQ Median UQ

  14. Outlier 1 8 9 10 10 11 12 13 13 15 27 IQR = 13 – 9 = 4 LQ Median UQ 9 – 1.5(4) = 3

  15. Outlier 1 8 9 10 10 11 12 13 13 15 27 IQR = 13 – 9 = 4 LQ Median UQ 9 – 1.5(4) = 3 Outlier

  16. Outlier 1 8 9 10 10 11 12 13 13 15 27 IQR = 13 – 9 = 4 LQ Median UQ 9 – 1.5(4) = 3 13 + 1.5(4) = 19 Outlier

  17. Outlier 1 8 9 10 10 11 12 13 13 15 27 IQR = 13 – 9 = 4 LQ Median UQ 9 – 1.5(4) = 3 13 + 1.5(4) = 19 Outlier Outlier

  18. Find Measures of Central Tendency and Variation

  19. Find Measures of Central Tendency and Variation • Mean 80.1 + 80.5 + 81.6 + 82.8 + 84.7 + 86.5 + 87.5 + 88.7 + 88.5 + 86.9 + 84.1 + 81.2 12 1013.1 12 84.425

  20. Find Measures of Central Tendency and Variation • Median 80.1, 80.5, 81.2, 81.6, 82.8, 84.1, 84.7, 86.5, 86.9, 87.5, 88.5, 88.7 84.1 and 84.7 84.1 + 84.7 2 168.8 2 84.4

  21. Find Measures of Central Tendency and Variation • Mode No mode • Range 88.7 – 80.1 = 8.6

  22. Find Measures of Central Tendency and Variation 80.1, 80.5, 81.2, 81.6, 82.8, 84.1, 84.7, 86.5, 86.9, 87.5, 88.5, 88.7 • Lower Quartile 81.2 + 81.6 = 162.8 162.8 ÷ 2 = 81.4 • Upper Quartile 86.9 + 87.5 = 174.4 174.4 ÷ 2 = 87.2

  23. Find Measures of Central Tendency and Variation • IQR 87.2 – 81.4 = 5.8 • Outlier 81.4 – 1.5(5.8) = 72.7 87.2 + 1.5(5.8) = 95.9 No outliers

  24. Guided Practice • Find the measures of central tendency and variation for the information in the table.

  25. Guided Practice

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