Curriculum
Course: Statistics — Third Secondary
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Curriculum

Statistics — Third Secondary

Unit 1: Correlation and Regression

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Unit 2: Advanced Statistical Measures

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Unit 3: Probability

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Unit 4: Random Variables

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Unit 5: The Normal Distribution

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Text lesson

Advanced Measures of Dispersion

Statistics — Third Secondary

Advanced Measures of Dispersion

Range, variance and standard deviation

Range, variance and standard deviation

  • Measures of dispersion show how far the values are spread out from each other or from their mean.
  • Measures of central tendency alone are not enough to describe data.
  • Two sets can have the same mean but very different spreads.
  • For example, the sets (49, 50, 51) and (10, 50, 90) both have a mean of 50, but their spreads are completely different.
Comparison aspectMain ideaKeywords
Range
  • Range = largest value − smallest value. It is easy to calculate
  • but it depends on only two values
largestvaluesmallesteasy
Variance σ²
  • the mean of the squared deviations from the mean
  • σ² = Σ(x − x̄)² ÷ n. It can also be calculated by the shortcut σ² = Σx² ÷ n − (x̄)²
meansquareddeviationscalculated
Standard deviation σ
  • the positive square root of the variance
  • σ = √σ². It is the most important measure of dispersion because it is in the same unit as the original data
positivesquarerootvariance
•
  • A smaller standard deviation means the data are more consistent and closer together. If σ = 0
  • all the values are equal
smallerstandarddeviationmeans
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