Frequency Distributions “ A Picture is Worth a Thousand Words ”

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# Frequency Distributions A Picture is Worth a Thousand Words - PowerPoint PPT Presentation

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”

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
• Connect using straight lines; include next highest and next lowest
• Especially useful with overlapping 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
• 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
• 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
• 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
• 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
• 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 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
• 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 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
• 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