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Standard Deviation Calculator

Standard deviation measures how spread out data is around the mean.

Calculated Result
2.13809

Standard deviation

Standard deviation (sample)

2.13809

Variance

4.571429

Mean

5

Count (n)

8

Sum

40

Min / Max

2 / 9

Range

7

2.1381 — Std. dev.

Calculation Breakdown

  1. Meanx̄ = Σx / n = 5
  2. Sample variances² = Σ(x − x̄)² / (n − 1) = 4.571429
  3. Standard deviations = √s² = 2.13809

Value vs Mean (2,4,4,4,5,5,7,9)

Interactive visualization based on your current inputs

Calculated Value
0.02.34.56.89.0245 (mean)79

What Is the Standard Deviation Calculator?

Standard deviation quantifies the dispersion of data around the mean.

How Does the Standard Deviation Calculator Work?

Compute mean, then square each deviation, average them (sample uses n-1), then take square root.

Standard Deviation Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

s=∑(xi−xˉ)2n−1s = \sqrt{\dfrac{\sum(x_i - \bar{x})^2}{n-1}}

Sample standard deviation divides by n−1 (Bessel's correction); population divides by n.

How to Use the Standard Deviation Calculator

  1. Enter numbers separated by commas, choose sample or population, and read all stats.

Step-by-Step Example Calculation

Sample SD of 2,4,4,4,5,5,7,9

Input Values:

numbers:2,4,4,4,5,5,7,9
type:sample
Worked Steps: Mean = 5, Sample SD = 2.

Understanding Your Result

Lower SD = data clustered near mean. Higher SD = more spread.

Factors That Affect the Result

  • Outliers increase SD significantly.

When Should You Use This Calculator?

  • Quality control, test scores, financial risk, scientific experiments.

Assumptions & Limitations

  • Use sample SD when the list is a sample from a larger population.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Computed using the two-pass algorithm for numerical stability.

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