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FREQUENCY DISTRIBUTIONS

FREQUENCY DISTRIBUTIONS. raw score distribution: list of each individual’s score frequency distribution: list of each score that appears and how many times each score occurs. Uses of Frequency Distributions. Summarize a large set of data. Describe the shape of a distribution.

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FREQUENCY DISTRIBUTIONS

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  1. FREQUENCY DISTRIBUTIONS • raw score distribution: list of each individual’s score • frequency distribution: list of each score that appears and how many times each score occurs

  2. Uses of Frequency Distributions • Summarize a large set of data. • Describe the shape of a distribution. • Needed for inferential statistics.

  3. A Raw Score Distribution 7 5 3 1 7 2 3 5 2 6 6 2 3 4 7 7 5 3 1 4 2 6 1 4 5 7 2 4 3 4 2 2 1 1 3 5 5 3 2 4 2 3 5 1 4 4 2 1 3 5

  4. Frequency Distribution Table x f 7 5 6 3 5 8 4 8 3 9 2 10 1 7

  5. 15 f 10 5 0 1 2 3 4 Frequency Polygon Best for quantitative/continuous data. Study Time in Hours

  6. 15 f 10 5 0 1 2 3 4 Histogram Best for quantitative/continuous data. Study Time in Hours

  7. Bar Graph Best for qualitative/discrete variables. 15 f 10 5 Ed. Bus. A&S AST College

  8. Guidelines for Graphs • Label units. • Make axes proportional (y axis should be 2/3 to 3/4 length of x axis). • Make bars equal width. • Keep it simple.

  9. Describing Frequency Distributions symmetrical: same on both sides

  10. skewed: scores piled on one side body tail positive skew negative skew

  11. kurtosis: steepness leptokurtic platykurtic mesokurtic

  12. Frequency Distribution Statistics • relative frequency: proportion of scores that are x • cumulative frequency: number of scores up to and including x • percentile rank: percentage of scores up to and including x • percentile: x score at a percentile rank

  13. Cumulative Frequency x f cf 7 5 50 6 3 45 5 8 42 4 8 34 3 9 26 2 10 17 1 7 7 always equals N, total # of scores add the frequencies start at the bottom score

  14. Relative Frequency divide each frequency by N x f rf 7 5 .10 6 3 .06 5 8 .16 4 8 .16 3 9 .18 2 10 . 20 1 7 .14 5/50 = .10 3/50 = .06 8/50 = .16 8/50 = .16 9/50 = .18 10/50 = .20 7/50 = .14

  15. Percentile Rank divide cf by N and multiply by 100 x f cf pr 7 5 50 100 6 3 45 90 5 8 42 84 4 8 34 68 3 9 26 52 2 10 17 34 1 7 7 14 100th %ile = 7 90th %ile = 6 84th %ile = 5 68th %ile = 4 52nd %ile = 3 34th %ile = 2 14th %ile = 1

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