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2.5-Measures of Position

2.5-Measures of Position. Fractiles : numbers that partition or divide an ordered data set into equal parts. Quartiles: 4=parts: Q ₁,Q₂,Q₃ Deciles: 10=parts: D₁,D₂,…D₉ Percentiles: 100=parts: P₁,P₂,…P₉₉. Quartiles: 4 = Parts: Q ₁, Q₂, Q₃ (Data in numerical order First).

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2.5-Measures of Position

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  1. 2.5-Measures of Position • Fractiles: numbers that partition or divide an ordered data set into equal parts. • Quartiles: 4=parts: Q₁,Q₂,Q₃ • Deciles: 10=parts: D₁,D₂,…D₉ • Percentiles: 100=parts: P₁,P₂,…P₉₉

  2. Quartiles: 4 = Parts: Q₁, Q₂, Q₃(Data in numerical order First) • First Quartile: Q₁ : • Middle of lowest half of data • Second Quartile: Q₂ = MEDIAN • Middle of all data • Third Quartile: Q₃ • Middle of upper half of data • Interquartile Range (IQR) : Q₃ - Q₁ • Variance of middle half of data

  3. Box and Whisker Plot • An Exploratory Data Analysis (EDA) to display quartiles • Identify the FIVE NUMBER SUMMARY • 1) minimum entry (left whisker) • 2) Q₁ (left side of box) • 3) Q₂ = median (Middle of box) • 4) Q₃ (Right side of box) • 5) maximum entry (right whisker) • Graph above a uniform number line

  4. Example: Find Q₁,Q₂,Q₃, IQR, and graph a box and whisker plot 13,9,18,15,14,21,7,10,11,20,5,18,37,16,17

  5. Example: Find Q₁,Q₂,Q₃, IQR, and graph a box and whisker plot 13,9,18,15,14,21,7,10,11,20,5,18,37,16,17 5,7,9,10,11,13,14,15,16,17,18,18,20,21,37

  6. Example: Find Q₁,Q₂,Q₃, IQR, and graph a box and whisker plot 13,9,18,15,14,21,7,10,11,20,5,18,37,16,17 5,7,9,10,11,13,14,15,16,17,18,18,20,21,37 Q₂

  7. Example: Find Q₁,Q₂,Q₃, IQR, and graph a box and whisker plot 13,9,18,15,14,21,7,10,11,20,5,18,37,16,17 5,7,9,10,11,13,14,15,16,17,18,18,20,21,37 Q₁ Q₂ Q₃

  8. Example: Find Q₁,Q₂,Q₃, IQR, and graph a box and whisker plot 13,9,18,15,14,21,7,10,11,20,5,18,37,16,17 5,7,9,10,11,13,14,15,16,17,18,18,20,21,37 Q₁ Q₂ Q₃ IQR = 18-10 =8

  9. Example: Find Q₁,Q₂,Q₃, IQR, and graph a box and whisker plot 13,9,18,15,14,21,7,10,11,20,5,18,37,16,17 5,7,9,10,11,13,14,15,16,17,18,18,20,21,37 Q₁ Q₂ Q₃ IQR = 18-10 =8 10 37 5 18 15

  10. Example: Find Q₁,Q₂,Q₃, IQR, and graph a box and whisker plot 13,9,18,15,14,21,7,10,11,20,5,18,37,16,17 5,7,9,10,11,13,14,15,16,17,18,18,20,21,37 Q₁ Q₂ Q₃ IQR = 18-10 =8 If 2 numbers are at a quartile, add/2 10 37 5 18 15

  11. Example: Find Q₁,Q₂,Q₃, IQR, and graph a box and whisker plot 20,26,28,25,31,14,23,15,12,26,29,24,31,19

  12. Example: Find Q₁,Q₂,Q₃, IQR, and graph a box and whisker plot 20,26,28,25,31,14,23,15,12,26,29,24,31,19 12,14,15,19,20,23,24,25,26,26,28,29,31,31

  13. Example: Find Q₁,Q₂,Q₃, IQR, and graph a box and whisker plot 20,26,28,25,31,14,23,15,12,26,29,24,31,19 12,14,15,19,20,23,24,25,26,26,28,29,31,31

  14. Example: Find Q₁,Q₂,Q₃, IQR, and graph a box and whisker plot 20,26,28,25,31,14,23,15,12,26,29,24,31,19 12,14,15,19,20,23,24,25,26,26,28,29,31,31 (24+25)/2 Q₂=24.5

  15. Example: Find Q₁,Q₂,Q₃, IQR, and graph a box and whisker plot 20,26,28,25,31,14,23,15,12,26,29,24,31,19 12,14,15,19,20,23,24 25,26,26,28,29,31,31 Q₁ (24+25)/2 Q₃ Q₂=24.5

  16. Example: Find Q₁,Q₂,Q₃, IQR, and graph a box and whisker plot 20,26,28,25,31,14,23,15,12,26,29,24,31,19 12,14,15,19,20,23,24 25,26,26,28,29,31,31 Q₁ (24+25)/2 Q₃ Q₂=24.5 IQR= 28-19= 9

  17. Example: Find Q₁,Q₂,Q₃, IQR, and graph a box and whisker plot 20,26,28,25,31,14,23,15,12,26,29,24,31,19 12,14,15,19,20,23,24 25,26,26,28,29,31,31 Q₁ (24+25)/2 Q₃ Q₂=24.5 IQR= 28-19= 9 19 31 12 28 24.5

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