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Variance Calculator

Enter your dataset values, and the calculator will instantly compute their variance (sample or population), coefficient of variation, and sum of squares, displaying detailed calculations.

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Variance Calculator

An online variance calculator helps determine variance, sum of squares, and coefficient of variance for a dataset. It also displays mean and standard deviation through step-by-step calculations.

What is Variance?

Variance measures how spread out the numbers in a dataset are. It is the average of the squared differences from the mean. Low variance indicates data points are close to the mean, while high variance shows greater spread.

Types of Variance

Sample Variance: Calculated from a sample (subset) of the population.
Population Variance: Calculated using the entire population.

Use an online Standard Deviation Calculator to quickly determine σ and other statistical measures.

Variance Formulas

Population Variance Formula:

σ² = Σ(x_i - μ)² / N

σ² = Population variance
μ = Population mean
x_i = Each data point
N = Total number of data points

Steps to calculate population variance:

Find deviation of each point from mean: x_i - μ
Square each deviation: (x_i - μ)²
Take the average of squared deviations: Σ(x_i - μ)² / N

Sample Variance Formula:

s² = Σ(x_i - x̄)² / (N - 1)

s² = Sample variance
x̄ = Sample mean
x_i = Each data point in sample
N = Number of observations in the sample

How to Calculate Variance

Find the mean (x̄) = Σ x_i / n
Calculate squared deviation: (x_i - x̄)²
Sum squared deviations: S = Σ(x_i - x̄)²
Calculate variance:
- Population: σ² = Σ(x_i - μ)² / N
- Sample: s² = Σ(x_i - x̄)² / (n - 1)

Online calculators perform these steps automatically and provide additional measures like mean, median, mode, and range via the Mean Median Mode Range Calculator.

Example:

Calculate the variance of exam scores: 50, 75, 89, 93, 93.

Mean: x̄ = (50 + 75 + 89 + 93 + 93) / 5 = 80
Deviation & Squared Deviation:

Score	Deviation from mean	Squared deviation
50	-30	900
75	-5	25
89	9	81
93	13	169
93	13	169

Variance: σ² = (900 + 25 + 81 + 169 + 169) / 5 = 268.8

How Variance Calculator Works

Input:

Enter dataset values separated by commas
Select sample or population
Click calculate to generate results

Output:

Variance, standard deviation, count, sum, mean, coefficient of variance, and sum of squares
Step-by-step calculations

FAQ

Difference between standard deviation and variance:

Variance is the average squared deviation from the mean, while standard deviation is its square root. SD is in the same units as the data; variance is in squared units.

Is high variance good or bad?

Low variance indicates stability, while high variance shows greater spread and risk. It depends on context and risk tolerance.

Range of variance:

The range = max value - min value. Extreme values strongly influence it.

Conclusion

Use this online variance calculator to compute sample and population variance quickly and accurately, with step-by-step explanations.

Other Languages: Varyans Hesaplama, Calculadora De Variancia, Kalkulator Varians, Kalkulator Wariancji, Výpočet Rozptylu, Калькулятор Дисперсии, 分散計算

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