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Variance and Standard Deviation
High School
Definition
Variance measures how spread out data is from the mean. Standard deviation is the square root of variance.
Formulas
Var(X) = E[(X - μ)²] = E[X²] - (E[X])²
Variance definition
σ = √Var(X)
Standard deviation
Var(aX + b) = a² Var(X)
Variance property
Examples
Example 1
Find the variance of {1, 2, 3, 4, 5}.
Applications
Finance
Investment risk measurement
Quality Control
Product consistency
Experimental Science
Measurement error analysis
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