frequency distributions a picture is worth a thousand words
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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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graphing techniques
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
types of frequency distributions
Types of Frequency Distributions
  • Normal distribution or normal curve
  • Highest scores in the middle
  • Tails are the extreme scores
  • Smooth line
  • Overlapping distribution
variations in normal distribution
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
remember plot data
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
simple frequency distribution
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
example of a simple frequency distribution
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
relative frequency distribution
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
example of a simple frequency distribution16
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
cumulative frequency distributions
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
example of a simple frequency distribution19
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
percentile
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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