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Frequency Distributions “ A Picture is Worth a Thousand Words ”

Frequency Distributions “ A Picture is Worth a Thousand Words ”. Chapter 3 Heiman. Graphing Techniques. Bar graph For nominal and ordinal data the adjacent bars should not touch Histogram For interval and ratio data the adjacent bars should touch Frequency polygon

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Frequency Distributions “ A Picture is Worth a Thousand Words ”

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  1. Frequency Distributions“A Picture is Worth a Thousand Words” Chapter 3 Heiman

  2. Graphing Techniques • Bar graph • For nominal and ordinal data the adjacent bars should not touch • Histogram • For interval and ratio data the adjacent bars should touch • Frequency polygon • Connect using straight lines; include next highest and next lowest • Especially useful with overlapping distributions

  3. Types of Frequency Distributions • Normal distribution or normal curve • Highest scores in the middle • Tails are the extreme scores • Smooth line • Overlapping distribution

  4. Variations in Normal Distribution • Mesokurtic = normal distribution • Leptokurtic = thin • Platykurtic = broad or fat • Skewed distributions • Negatively skewed: low frequency of low scores and higher frequency of high scores • Positively skewed: low frequency of high scores and higher frequency of low scores • Bimodal distribution • rectangular distribution

  5. Remember: Plot Data • Distribution • See the pattern • N = number of scores/sample size • f = Frequency with which the different scores occur • What scores occurred and how often • Create a table before plotting

  6. Simple Frequency Distribution • The number of times that score occurs • Make a table with highest score at top and decreasing for every possible whole number • N (total number of scores) always equals the sum of the frequency • f = N

  7. Example of a simple frequency distribution • 5 7 8 1 5 9 3 4 2 2 3 4 9 7 1 4 5 6 8 9 4 3 5 2 1 • f • 9 3 • 8 2 • 7 2 • 6 1 • 5 4 • 4 4 • 3 3 • 2 3 • 1 3 • f = 25

  8. Relative Frequency Distribution • Proportion of the total N • Divide the frequency of each score by N • Rel. f = f/N • Sum of relative frequencies should equal 1.0 • Gives us a frame of reference • Find relative frequency using the normal curve • Proportion of the total area under the curve

  9. Example of a simple frequency distribution • 5 7 8 1 5 9 3 4 2 2 3 4 9 7 1 4 5 6 8 9 4 3 5 2 1 • f rel f • 9 3 .12 • 8 2 .08 • 7 2 .08 • 6 1 .04 • 5 4 .16 • 4 4 .16 • 3 3 .12 • 2 3 .12 • 1 3 .12 • f = 25  rel f = 1.0

  10. Cumulative Frequency Distributions • cf = cumulative frequency: number of scores at or below a particular score • A score’s standing relative to other scores • Count from lower scores and add the simple frequencies for all scores below that score

  11. Example of a simple frequency distribution • 5 7 8 1 5 9 3 4 2 2 3 4 9 7 1 4 5 6 8 9 4 3 5 2 1 • f rel f cf • 9 3 .12 25 • 8 2 .08 22 • 7 2 .08 20 • 6 1 .04 18 • 5 4 .16 17 • 4 4 .16 13 • 3 3 .12 9 • 2 3 .12 6 • 1 3 .12 3 • f = 25  rel f = 1.0

  12. Percentile • Percent of all scores in the data that are at or below a certain point • Takes into consideration the sample N • Convert cumulative frequency into percents

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