Dispersion Measures Calculator

Enter Dataset Values

Dataset

Enter numbers separated by commas, spaces, semicolons, or new lines.

Preferred delimiter Variance basis Decimal places

Included outputs

Variance and standard deviation
Range, quartiles, and interquartile range
Mean and median absolute deviation
Coefficient of variation and percentile range
CSV and PDF result exports

Example Data Table

Use this sample dataset to test the calculator quickly.

Observation	Value	Deviation from Mean	Absolute Deviation	Squared Deviation
1	12	-9.3	9.3	86.49
2	15	-6.3	6.3	39.69
3	18	-3.3	3.3	10.89
4	19	-2.3	2.3	5.29
5	22	0.7	0.7	0.49
6	23	1.7	1.7	2.89
7	23	1.7	1.7	2.89
8	24	2.7	2.7	7.29
9	27	5.7	5.7	32.49
10	30	8.7	8.7	75.69

Formula Used

Range: Maximum − Minimum

Sample variance: Σ(x − x̄)² / (n − 1)

Population variance: Σ(x − μ)² / n

Standard deviation: √Variance

Interquartile range: Q3 − Q1

Mean absolute deviation: Σ|x − x̄| / n

Median absolute deviation: Median(|x − Median|)

Coefficient of variation: (Standard Deviation / |Mean|) × 100

These measures describe how tightly or loosely values cluster around a center. Lower spread usually indicates more consistent observations, while higher spread signals greater variability.

How to Use This Calculator

Paste or type your dataset into the value box.
Select automatic detection or choose a preferred delimiter.
Choose sample variance for sample data or population variance for full populations.
Set the decimal precision that matches your reporting standard.
Press Calculate Dispersion to display results above the form.
Download the result summary in CSV or PDF format when needed.

Frequently Asked Questions

1. What does a dispersion measure show?

It shows how widely observations spread around a central value. Small dispersion suggests consistency, while large dispersion indicates broader variation within the dataset.

2. When should I use sample variance?

Use sample variance when your data represents only part of a larger population. The formula divides by n − 1 to reduce bias in estimation.

3. When is population variance better?

Use population variance when your dataset contains every observation in the group you want to describe. It divides by n.

4. Why is standard deviation so common?

Standard deviation is easy to interpret because it uses the original unit scale. That makes it practical for reporting risk, consistency, and process variation.

5. What is the advantage of IQR?

The interquartile range focuses on the middle fifty percent of values. It resists extreme outliers better than range and often supports robust exploratory analysis.

6. Why can coefficient of variation be undefined?

It becomes undefined when the mean is zero because the formula divides by the absolute mean. Near-zero means can also produce unstable percentages.

7. Can I compare two datasets with different units?

Yes, coefficient of variation often helps because it standardizes spread relative to the mean. Still, ensure both datasets are conceptually comparable first.