Lesson 4 of 11 · All lessons in this module
- Mean, median, mode and outliers
- Quantiles, box plots and their uses
- Range, mean absolute deviation, variance and standard deviation
- Median absolute deviation, semivariance and estimator bias
- Target downside deviation and coefficient of variationVideo lesson
- Returns not prices, data frequency and volatility scaling
- Skewness and kurtosisVideo lesson
- Scatter plots, covariance and correlation
- Limits of correlation analysis
- The four moments, benchmark correlation and spreadsheet functions
- Integrated cases: describing one return series from raw data
This lesson is part of the 2027 curriculum. You are following the 2026 curriculum, where it is not taught in this form. Switch if you are sitting the exam under the 2027 curriculum.
Lesson 4 of 11 · 12 min
Median absolute deviation, semivariance and estimator bias
Two more ways to measure spread, one robust to outliers and one that looks only below the mean, plus why a sample standard deviation still tends to understate the true one.
In short
- The median absolute deviation is the median of the absolute distances from the median: a robust dispersion measure that outliers barely move.
- Semivariance is the variance of the observations below the mean only; its square root is the semideviation.
- Population variance divides by N around the population mean μ; sample variance divides by n − 1 around . The n − 1 is Bessel's correction.
- Bessel's correction makes the sample variance unbiased, but the sample standard deviation stays biased: on average it understates σ.
- The bias matters most in small samples with high dispersion; beyond roughly 100 observations it fades.
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