Statistics

Standard Deviation Formula - Statistics

Learn the standard deviation formula with examples, step-by-step guide, and calculator tools. Measure the amount of variation in a set of values

The standard deviation formula is a fundamental concept in statistics. Measure the amount of variation in a set of values. This page provides a comprehensive guide with worked examples and practical applications.

The Formula

\[\sigma = \sqrt{\frac{1}{n}\sum_{i=1}^{n}(x_i - \bar{x})^2}\]

Variables

σ
Standard deviation
n
Number of values
xᵢ
Individual values
Mean of values

Step-by-Step Guide

  1. 1

    Step 1: Gather your data values

  2. 2

    Step 2: Apply the formula

  3. 3

    Step 3: Perform the calculations

  4. 4

    Step 4: Interpret the result

Examples

Example 1

Example 1: [2,4,6,8,10] → Standard Deviation = √8 = 2.83

Example 2

Example 2: 2.83

Frequently Asked Questions

What is the standard deviation formula?

Measure the amount of variation in a set of values

How do I calculate standard deviation formula?

Use the formula: \sigma = \sqrt{\frac{1}{n}\sum_{i=1}^{n}(x_i - \bar{x})^2}. Follow the steps provided above.

What tools can help with standard deviation formula?

We provide online calculators: standard-deviation-calculator, variance-calculator

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