Standard Deviation Calculator

Calculate mean, variance, and standard deviation for any data set.

Enter Data Set

Data (8 values): 2, 4, 4, 4, 5, 5, 7, 9

Standard Deviation (s)

2.1381

Mean (Average)

5

Variance

4.5714

Median

4.5

Mode

4

Min / Max

2 / 9

Range

7

Standard Deviation Calculator Formula & How It Works

σ = √[Σ(xᵢ−μ)² / N] (population) | s = √[Σ(xᵢ−x̄)² / (N−1)] (sample)
  • μ or x̄ = mean of the data set
  • N = total number of data points
  • Population SD (σ): divide by N (know the whole population)
  • Sample SD (s): divide by N−1 (Bessel's correction for sample data)

Standard deviation measures the spread of data around the mean. Low SD → data points cluster close to the mean. High SD → data is spread out. Use population SD when you have the complete population data; use sample SD (with N−1) when your data is a sample from a larger population — this corrects for underestimation bias.

Standard Deviation Calculator FAQs

What does standard deviation tell you?

Standard deviation quantifies variability. In a normal distribution: 68% of data falls within ±1 SD of the mean; 95% within ±2 SD; 99.7% within ±3 SD (the 68-95-99.7 rule). A stock with SD of 20% is more volatile than one with SD of 5%.

When to use population vs sample standard deviation?

Population SD (divide by N): when you have data for the entire population (all students in a class, all employees). Sample SD (divide by N−1): when your data is a sample from a larger group (survey of 100 from 10,000 customers). When in doubt, use sample SD — it's more conservative.

What is variance vs standard deviation?

Variance = SD². Variance is in squared units (making it harder to interpret). Standard deviation is in the original units and easier to interpret. Variance is used in statistical formulas (e.g., ANOVA); SD is used for describing data spread.

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