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
- Enter data points representing the variable of interest.
- Review range, variance, standard deviation, IQR, MAD, and CV.
- Identify which dispersion metrics suit your analysis (robust vs. sensitive to outliers).
- 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.