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Population Variance Calculator

Calculate summary metrics, mean, median, mode, variance, standard deviation, quartiles, and correlation for population variance.

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Input Data Set

Enter comma-separated numbers for statistical analysis.

Calculated Metric Value

21.71 mean
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Statistical Rule

For symmetric distributions, Mean = Median. For skewed distributions, the median is more robust against extreme outliers than the mean.

Calculation Methodology & Details

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Formula

Sample Mean: x̄ = Σx / n Sample Variance: s² = Σ(x - x̄)² / (n - 1) Standard Deviation: s = √s²

Applies standard descriptive statistics definitions, Tukey 1.5×IQR outlier boundaries, and Pearson moment equations.

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Important Disclaimer

Calculations assume unweighted sample measurements unless weighted frequencies or grouped interval classes are specified.

How to Calculate Step-by-Step

Follow these steps to complete the calculation:

1

Step 1

Enter dataset values separated by commas, spaces, or line breaks.

2

Step 2

Select sample (n-1) vs population (N) variance mode or target percentile rank.

3

Step 3

View 5-number summary (Min, Q1, Median, Q3, Max), standard deviation, skewness, or outlier flags.

Detailed Insights & Expert Guide

ℹ️ About this Calculation

The Population Variance Calculator computes summary location statistics (mean, median, mode), dispersion metrics (range, IQR, variance, standard deviation), correlation (Pearson, Spearman), and shape moments (skewness, kurtosis).

Variable Glossary

Input

Data Points (x_i)

Numerical measurements collected in the sample observation vector.

Parameter

Degree of Freedom (n - 1)

Bessel's correction factor for unbiased sample variance estimation.

FAQ

How is an outlier detected using the 1.5×IQR Rule?
An observation is flagged as an outlier if it falls below the Lower Fence (Q1 - 1.5 × IQR) or above the Upper Fence (Q3 + 1.5 × IQR), where IQR = Q3 - Q1.
What is the 5-Number Summary?
The 5-Number Summary consists of five key order statistics: Minimum, First Quartile (25th percentile Q1), Median (50th percentile Q2), Third Quartile (75th percentile Q3), and Maximum.
What does the Coefficient of Variation (CV) measure?
Coefficient of Variation (CV = s / x̄ × 100%) measures relative dispersion, allowing comparison of variability between datasets measured in completely different units.