Variance Calculator: Easy-to-Use Statistical Tool for Data Analysis

How to use the tool

1. Type your observations in the Observations box, separated by spaces.
   Example A: 2 4 6 8
   Example B: 5.1 5.9 6.3 6.7 6.5
2. Click Calculate. The calculator validates every entry and needs at least two numbers.
3. Read the returned Mean and Sample Variance shown beneath the form.

Formulas used

Mean:

$$ \bar x = rac{\sum_{i=1}^{n}x_i}{n} $$

Sample variance (Bessel-corrected):

$$ s^2 = rac{\sum_{i=1}^{n}(x_i-\bar x)^2}{n-1} $$

Worked example: 2 4 6 8

• Mean: $$\bar x = rac{2+4+6+8}{4}=5$$
• Squared deviations sum: (9+1+1+9=20)
• Variance: $$s^2 = rac{20}{4-1}=6.6667$$

Worked example: 5.1 5.9 6.3 6.7 6.5

• Mean: $$\bar x = rac{30.5}{5}=6.1$$
• Squared deviations sum: (1.60)
• Variance: $$s^2 = rac{1.60}{5-1}=0.4000$$

Quick-Facts

• Sample variance uses (n-1) to stay unbiased (NIST e-Handbook, 2023).
• Variance units are the square of original units (ISO 3534-1:2006).
• Variance is always ≥ 0 because of squaring (NIST, 2023).
• Four-decimal display matches common lab reporting practice (ASTM E2586-10).

FAQ

What is variance?

Variance measures the average squared distance of each value from the mean (NIST, 2023).

Why divide by n – 1 instead of n?

“Using n – 1 yields an unbiased estimator of population variance” (Montgomery, 2019).

Can variance be negative?

No. Squaring deviations guarantees non-negative results (NIST, 2023).

How does variance relate to standard deviation?

Standard deviation is the square root of variance, expressed in the original measurement units (Walpole & Myers, 2017).

What data size gives reliable results?

At least 30 observations reduces sampling error in variance estimates (CLSI EP17, 2022).

Does data order matter?

Order is irrelevant; variance depends only on the set, not sequence (Weisstein, 2004).

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