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Statistics

Standard Deviation

Formula
σ = √(Σ(xᵢ − μ)² / N)

What is Standard Deviation?

Standard deviation measures how spread out the data is from the mean. A low standard deviation means the values are close to the mean; a high standard deviation means they are spread out.

Variables

  • σ
    σ — Standard deviation (population)
  • x
    xᵢ — Each data value
  • μ
    μ — Mean of the data
  • N
    N — Number of data values

Worked Examples

Example 1

Find the standard deviation of 2, 4, 4, 4, 5, 5, 7, 9.

Solution:

Mean = 5. Deviations: −3, −1, −1, −1, 0, 0, 2, 4. Squared: 9, 1, 1, 1, 0, 0, 4, 16. Sum = 32. σ = √(32/8) = √4 = 2

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