Dispersion Calculator — Range, Variance, Std Dev & IQR
Enter a list of numbers and instantly compute every key measure of spread: range, population and sample variance, standard deviation, IQR, mean absolute deviation, and the coefficient of variation.
Average distance of each data point from the mean
How does this calculator work?
Enter comma-separated numbers to compute: range (max−min), population variance σ²=Σ(x−μ)²/N, sample variance s²=Σ(x−x̄)²/(N−1), standard deviations σ and s, IQR=Q3−Q1 (middle 50% spread), mean absolute deviation, and coefficient of variation. IQR and MAD are more robust to outliers than variance.
Formula
How this is calculated
Measures of dispersion quantify how spread out a dataset is around its centre. The simplest is the range — the gap between the maximum and minimum values — but it is sensitive to outliers. Variance and standard deviation are the workhorses: each data point's squared deviation from the mean is averaged (population variance σ² divides by N; sample variance s² divides by N−1 to give an unbiased estimate when working from a sample). Taking the square root gives the standard deviation, restoring the original units.
The interquartile range (IQR = Q3 − Q1) is the spread of the middle 50% of the data. Because it ignores the top and bottom quarters entirely, it is robust to outliers and is the preferred spread measure alongside the median in skewed distributions. The mean absolute deviation (MAD) is another robust alternative — it averages the absolute (not squared) deviations from the mean, so extreme points have less influence than they do in variance.
The coefficient of variation (CV = σ / |μ| × 100%) expresses the standard deviation as a percentage of the mean. It is unitless, making it useful for comparing the relative spread of datasets measured on different scales or with different means.
Frequently asked questions
Use population variance (σ², dividing by N) when your data is the entire population. Use sample variance (s², dividing by N−1) when your data is a sample taken from a larger population — the N−1 denominator (Bessel's correction) produces an unbiased estimate of the true population variance.
The range only uses the two extreme values, so a single outlier can dramatically inflate it. The IQR measures the spread of the central 50% of data, making it robust to outliers and more representative of the typical spread in heavily skewed distributions.
The CV expresses standard deviation as a percentage of the mean, making it unitless. This lets you compare spread between datasets on different scales — for example, comparing variability of heights (in cm) and weights (in kg) is meaningless with raw standard deviations but fair with CV.
Also known as
TG we-Calculate Editorial Team. (2026). Dispersion Calculator — Range, Variance, Std Dev & IQR [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/dispersion-calculator
TG we-Calculate Editorial Team. "Dispersion Calculator — Range, Variance, Std Dev & IQR." TG we-Calculate. 2026. https://we-calculate.com/calculator/dispersion-calculator.
TG we-Calculate Editorial Team, "Dispersion Calculator — Range, Variance, Std Dev & IQR," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/dispersion-calculator
@misc{wecalculate_dispersion_calculator, title = {Dispersion Calculator — Range, Variance, Std Dev & IQR}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/dispersion-calculator}}, year = {2026}, note = {TG we-Calculate} }
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