A Practical Series on Measuring Variability, Spread, and Statistical Dispersion
Most introductory statistics courses teach a familiar sequence:
mean → variance → standard deviation.
That sequence is useful, but it can accidentally suggest that once we know the standard deviation, the problem of measuring variability has been solved.
It has not.
There are many legitimate meanings of "spread":
- How far apart are the extremes?
- How wide is the central half of the data?
- How far is a typical observation from the center?
- How different are two randomly selected observations?
- How variable is the quantity relative to its magnitude?
- How much of the spread is caused by rare observations?
- How dispersed is a multidimensional cloud?
- What does dispersion even mean for angles, compositions, probability distributions, networks, images, or embeddings?
Different measures answer different questions.
This series explores those questions mathematically, historically, computationally, and practically.
The posts are:
- What Does "Spread" Actually Mean?
- Range, IQR, and Absolute Deviations
- Variance and Standard Deviation: Why Squaring Won
- Relative Dispersion: CV, Fano Factor, and Scale-Free Measures
- Robust Dispersion: MAD, Qn, Sn, and Gini Mean Difference
- Comparing Dispersion Between Groups
- Multivariate and High-Dimensional Dispersion
- When Ordinary Variance Stops Making Sense
- Where Dispersion Research Could Go Next
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