the.com/variance
the math of how wildly things scatter before averages smugly claim everything was fine
means The statistical measure of how far a set of values spreads out from their mean, calculated as the average of the squared differences from that mean — and, more loosely, any difference or disagreement between things.
from From Latin 'variantia,' meaning difference or diversity, built on the verb 'variare,' to change or diversify, which itself comes from 'varius' — varied, mottled, speckled. The word arrived in English through Old French 'variance' in the medieval period, long carrying the everyday sense of disagreement or discrepancy (as in 'at variance with'). The precise statistical meaning is a much later graft: it was coined in the early 20th century by the statistician Ronald Fisher, who borrowed the ordinary word and pinned a hard mathematical definition onto it.
- units quirk
- measured in squared units, hence the stranger standard deviation
- never negative
- squaring guarantees it can only equal zero or rise
- additive trick
- independent variables let their variances simply add together
- finance fear
- investors call its square root volatility and lose sleep
- zero means
- variance of zero means every value is identical
levene's test — statistical test for equality of variances across groups, developed by henry levene in 1960
analysis of variance — anova method comparing means by analyzing variance, developed by ronald fisher in 1920s
chebyshev's inequality — bounds probability of variance deviation, states p(|x-μ|≥kσ) ≤ 1/k² for any k>0