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Chapter 2 Frequency Distributions and Graphs I Frequency Distributions for Quantitative Variables

Chapter 2 Frequency Distributions and Graphs I Frequency Distributions for Quantitative Variables A. Ungrouped Frequency Distribution 1. Each class interval contains a single score value. Table 1. Taylor Manifest Anxiety Scores (1) (2). 74 1 73 1 72 0 71 2 70 7

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Chapter 2 Frequency Distributions and Graphs I Frequency Distributions for Quantitative Variables

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  1. Chapter 2 • Frequency Distributions and Graphs • I Frequency Distributions for Quantitative Variables • A. Ungrouped Frequency Distribution • 1. Each class interval contains a single score value

  2. Table 1. Taylor Manifest Anxiety Scores • (1) (2) 74 1 73 1 72 0 71 2 70 7 69 8 68 5 67 2 66 1 65 1 n = 28

  3. 2. Class interval size, i i = score real upper limit – score real lower limit B. Grouped Frequency Distribution 1. Each class interval spans two or more score values

  4. Table 2. IQ Data (1) (2) Xjf 160–169 1 150–159 1 140–149 0 130–139 2 120–129 3 110–119 6 100–109 8 90–99 3 80–89 1 70–79 1 n = 26

  5. 2. Size of 100–109 class interval

  6. C. Conventions Used in Constructing Frequency Distributions D. Determining the Number and Size of Class Intervals By Trial and Error E. Pros and Cons of Grouping Data

  7. F. Relative Frequency Distributions Table 3. IQ Data (1) (2) (3) (4) Xj f Prop f % f 160–169 1 .04 4 150–159 1 .04 4 140–149 0 .00 0 130–139 2 .08 8 120–129 3 .12 12 110–119 6 .23 23 100–109 8 .31 31 90–99 3 .12 12 80–89 1 .04 4 70–79 1 .04 4 n = 26 1.00 100

  8. G. Cumulative Frequency Distributions Table 4. IQ Data (1) (2) (3) (4) (5) (6) Xjf Prop f % f Cum prop f Cum % 160–169 1 .04 4 1.00 100 150–159 1 .04 4 .98 98 140–149 0 .00 0 .94 94 130–139 2 .08 8 .94 94 120–129 3 .12 12 .86 86 110–119 6 .23 23 .74 74 100–109 8 .31 31 .51 51 90–99 3 .12 12 .20 20 80–89 1 .04 4 .08 8 70–79 1 .04 4 .04 4 n = 26 1.00 100

  9. II Frequency Distribution for Qualitative Variables Table 5. Leading Cause of Death of Men in 2006 XProp f Accidents .07 Cancer .22 Heart disease .38 Stroke .08 Other .25 Total 1.00

  10. A. Conventions Used in Constructing Frequency Distributions for Qualitative Variables III Graphs for Quantitative Variables A. Histogram for IQ Data

  11. B. Frequency Polygon for IQ Data

  12. C. Cumulative Polygon for IQ Data

  13. D. Stem-and-Leaf Display for IQ Data • (1) (2) (3) • StemsLeaves f • 70–79 8 1 • 80–89 5 1 • 90–99 3 8 6 3 • 100–109 7 1 8 2 9 5 4 3 8 • 110–119 6 2 3 5 6 8 6 • 120–129 2 9 7 3 • 130–139 3 5 2 • 140–149 0 • 150–159 2 1 • 160–169 0 1

  14. IV Graphs for Qualitative Variables A. Bar Graph for Leading Cause of Death of Men in 2006

  15. B. Pie Chart for Leading Cause of Death of Men in 2006

  16. 1. Construction of pie charts Conversion of Prop f To Minutes Accidents .07  60 = 4.2 Cancer .22  60 13.2 + 4.2 =17.4 Heart disease .38  60 22.8 + 17.4 = 40.2 Stroke .08  60 4.8+ 40.2 =45.0 Other .25  60 15.0+ 45.0 =60.0

  17. V Shapes of Distributions

  18. VI Misleading Graphs Figure 1. Two plots of the same data. Figure (a) is misleading.

  19. A. Pictogram Figure 2. Figure (a) is misleading because it uses both height and area to represent computer sales

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