Frequency Distributions A Picture is Worth a Thousand Words

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Frequency DistributionsA Picture is Worth a
Thousand Words

• Chapter 3
• Heiman

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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

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Types of Frequency Distributions

• Normal distribution or normal curve
• Highest scores in the middle
• Tails are the extreme scores
• Smooth line
• Overlapping distribution

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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

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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

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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

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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

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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

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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

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Cumulative Frequency Distributions

• cf cumulative frequency number of scores at or
  below a particular score
• A scores standing relative to other scores
• Count from lower scores and add the simple
  frequencies for all scores below that score

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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

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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