Dispersion Calculator

Enter a dataset to analyze spread metrics that describe variability and consistency.

Range

24.0000

Std. deviation (s)

8.2158

Coefficient of variation

34.23%

Detailed metrics

Count: 9

Mean: 24.0000

Sample variance: 67.5000

Mean absolute deviation: 6.6667

Q1: 18.0000

Q3: 30.0000

Interquartile range: 12.0000

Range: 24.0000

How to Use This Calculator

  1. Enter data points representing the variable of interest.
  2. Review range, variance, standard deviation, IQR, MAD, and CV.
  3. Identify which dispersion metrics suit your analysis (robust vs. sensitive to outliers).
  4. Compare multiple datasets by repeating the process and evaluating differences in spread.

Formula

Range = max − min

Sample variance (s²) = Σ(xi − μ)² / (n − 1)

Standard deviation (s) = √(s²)

Mean absolute deviation = Σ|xi − μ| / n

Coefficient of variation = (s / μ) × 100%

Interquartile range (IQR) = Q3 − Q1

Dispersion metrics quantify variability and stability, aiding risk assessment, quality control, and exploratory analysis.

Full Description

Measures of dispersion complement central tendency by revealing how widely values spread around the mean or median. This calculator highlights both variance-based metrics (sensitive to outliers) and robust measures such as IQR and MAD.

Choose metrics based on your domain: manufacturing may rely on standard deviation, while finance and forecasting often examine CV and MAD.

Frequently Asked Questions

Which metric is most robust to outliers?

Interquartile range and mean absolute deviation are less sensitive to extreme values than variance or standard deviation.

Why calculate coefficient of variation?

CV expresses variability relative to the mean, enabling comparisons across scales or units.

Do I need a minimum number of values?

At least two observations are required for sample variance and standard deviation; more data improves reliability.

Can I use this with negative numbers?

Yes. Dispersion metrics handle negative values as long as the dataset contains real numbers.