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
Expectation and Variance
Expectation and Variance
Variance and standard deviation
Variance and standard deviation
- The variance σ² measures how much the values of the variable spread out around the expectation.
- It can be calculated by the shortcut formula:
σ² = Σ (x² × f(x)) − μ²
- The standard deviation σ is the positive square root of the variance.
- To calculate these quantities we use a table with four columns:
Key points
Column 1the values x.
Column 2the probabilities f(x), whose sum equals 1.
Column 3x × f(x). Its sum is the expectation μ.
Column 4x² × f(x). Its sum is Σ x² f(x).
- Then we calculate the variance σ² = (sum of column 4) − μ²
- and the standard deviation σ = √σ².
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