Frequency Distributions and Graphs

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Frequency Distributions and Graphs

• Summarize a set of scores
• Two columns
• Scores X
• Highest to lowest scores inclusive
• Frequency f
• Number of occurrences of each score

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• Sample size
• Sum of scores
• Proportion
• Percent

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Grouped Frequency Distributions

• Many scores group the data in class intervals
• Score columncategories
• f number of scores in each interval
• Rules
• 5-15 categories, 10 average
• Intervals equal in size
• 2, 3, 5, and multiples of 5 preferred
• Extreme categories include extreme scores
• Lowest interval starting with lowest multiple of
  the interval width equal to or less than the
  lowest score.
• Real limits of an interval constitute the limits
  of the interval, not the apparent limits
• Loss of information

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Graphing Data

• Fundamentals
• Two axes
• Horizontal axis-x axis-abscissa
• Scores or independent variable
• Vertical axis-y axis-ordinate
• Frequencies or dependent variable
• Origin0,0.
• Labeled, unit of measure specified
• Interval/ratio data frequency distributions
• Histogramsbars touching, height represents
  frequency
• Frequency polygonsconnecting midpoint of the top
  of each bar
• Midpoint
• Nominal/ordinal data
• Bar graphbars don't touch

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Distributions

• Population distribution graphs
• Relative frequencies
• Smooth curves

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Distribution Shape

• Symmetrical distributions, both halves match
• Skewed distributions scores pile up at one end or
  the other
• Positive skewmost scores low, tail pointing
  towards the high end
• Negative skewmost scores high, tail pointing
  towards the lower end

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Percentile Ranks

• Percentile rankspercentage of scores at or below
  a given score
• Cumulative frequency (cf) number of the scores
  are at or below a given score or interval
• Percentile rank

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Stem and Leaf

• Stem and Leaf
• First digit(s) stem
• Leavesfinal digit