Calculator Paradise

    Standard Deviation Formula

    Standard deviation measures how spread out numbers are from the mean. A low SD means data points cluster near the average; a high SD means they're spread out.

    Population Standard Deviation

    σ = √[Σ(xi - μ)² / N]

    Where:

    • σ = Standard deviation
    • xi = Each data point
    • μ = Mean (average)
    • N = Number of data points

    Step-by-Step:

    1. 1

      Find the mean

      Sum all values and divide by count.

    2. 2

      Subtract mean from each value

      Calculate (xi - μ) for each data point.

    3. 3

      Square each difference

      Square all the deviations.

    4. 4

      Average and square root

      Sum the squares, divide by N, take square root.

    Worked Examples:

    Test scores

    Data: 85, 90, 78, 92, 88

    Result: SD = 4.86

    Mean = 86.6. Deviations: -1.6, 3.4, -8.6, 5.4, 1.4. Squared sum = 114.8. Variance = 22.96. SD = √22.96 = 4.79

    Frequently Asked Questions