Dispersion Calculator

What Is Statistical Dispersion?

Dispersion describes how spread out data values are around a center. Low dispersion means values cluster tightly; high dispersion means they are scattered. This calculator reports range, variance, standard deviation, IQR, and quartile deviation alongside central tendency measures. Compare with the Standard Deviation Calculator and Mean Median Mode Range Calculator.

Key Dispersion Formulas

Range: $\text{max} - \text{min}$. Midrange: $(\text{max} + \text{min}) / 2$. IQR: $Q_3 - Q_1$. Quartile deviation: $\text{IQR} / 2$. Variance (sample): $\sum(x - \bar{x})^2 / (n - 1)$. Standard deviation is the square root of variance.

When to Use Dispersion

Two datasets can share the same mean but differ greatly in spread. Dispersion helps compare variability across groups, assess measurement precision, and decide whether averages alone tell the full story.

Frequently Asked Questions

What is the difference between range and IQR?

Range uses only the minimum and maximum. IQR uses the middle 50% of data (Q1 to Q3) and is less sensitive to extreme outliers.

What is quartile deviation?

Quartile deviation is half the IQR. It measures average distance from the median within the central half of the data.

Sample vs population variance?

Sample variance divides by $n-1$ for unbiased estimation from a subset. Population variance divides by $n$ when you have the full group.

How many values do I need?

At least two numeric values. More data gives more reliable dispersion estimates.

Why compare dispersion across datasets?

Dispersion reveals whether two groups with similar averages actually behave similarly. A teacher and an engineer might earn similar means but very different spreads.

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What Is Statistical Dispersion?

Key Dispersion Formulas

When to Use Dispersion

Frequently Asked Questions

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