Range

1
Range
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Descriptive Statistics and Describing the
Characteristics of a Distribution

• Averages are only half of the story
• The other half is measures of variability

3
Variability

• Reflects how scores differ from one another
• 7, 6, 3, 3, 1
• 3, 4, 4, 5, 4
• 4, 4, 4, 4, 4

What is the average?
X4 Some Variability
What is the average?
X4 Less Variability
What is the average?
X4 No Variability
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Variability (cont.)

• Can also be called spread or dispersion
• The smaller the dispersion (or variability), the
  more reliable the mean
• If the variability is small
• The mean is considered quite representative of
  the data
• The mean is a reliable average
• Conversely, if there is a large variability, the
  mean is not very reliable

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Variability (cont.)

• Can be thought of as a measure of how different
  scores are from one another
• Think of it as How different scores are from one
  particular score

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Variability (cont.)

• What score are we talking about?
• The mean.
• Variability becomes a measure of how much each
  score in a group of scores differs from the mean

7
Variability (cont.)

• The average is a representative score in a set of
  scores
• Now think about variability
• Variability reflects how different scores are
  from one another
• Together the average and the variability can
  describe the characteristics of a distribution
  and show how distributions differ from one antoher

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Variability (cont.)

• Three measures of variability reflect the degree
  of variability, spread, or dispersion in a group
  of scores
• Range
• Standard deviation
• Variance

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Range

• Most general measure of variability
• Gives you an idea of how far apart scores are
  from one another
• Computed by subtracting the lowest score from the
  highest score
• r h l
• r range h highest score llowest score

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Range (cont.)

• Is used to get a very general estimate of how
  wide or different scores are from one another
• How much spread there is from the lowest to the
  highest point in a distribution
• Should not be used to reach any conclusions
  regarding how individual scores differ from one
  another.