Variance is the second central moment of a random variable or probability distribution: Var(X) = E[(X - E[X])^2] = E[X^2] - (E[X])^2. Its parameters are a probability space and a real-valued random variable X with finite second moment; for a discrete distribution with mass p_i at x_i and mean mu, Var = sum_i p_i (x_i - mu)^2. It persists as the standard dispersion functional of probability and statistics: computed by statistical software, propagated through moment algebra (linearity of covariance, law of total variance), and carried in every probability and statistics curriculum as the canonical measure of spread about the mean. [formal: variance | substrate: mind | horizon: as-long-as-us | explicit: yes | epoch: 0.99]
Accepted ontology entry
variance
Variance is the second central moment of a random variable or probability distribution: Var(X) = E[(X - E[X])^2] = E[X^2] - (E[X])^2. Its parameters are a probability space and a real-valued random variable X with finite second moment; for…
Definition
Why it is in scope
The second central moment of a random variable, quantifying the expected squared deviation of outcomes from their mean — a human-made mathematical construct for measuring dispersion in probability distributions.
Names and aliases
- varianceen · CANONICAL
Relations from this entry
- cmsdard4403ny3vv3nkbt821lDEPENDS_ON →
Variance Var(X) = E[(X − E[X])²] is a functional of a probability distribution. Remove the probability distribution and variance has no mathematical object to operate on — it ceases to exist. Direction correct: variance (epoch 0.99) depends on probability distribution (epoch 0), the most foundational construct. Variance is the second central moment, a specific functional computed from the distribution.
- cmsmr9nmp023q1q13rk6xnpgeINSTANCE_OF →
Variance is a specific statistical measure: a human-constructed quantitative metric that summarizes dispersion of a distribution. A competent speaker would call variance 'a statistical measure'.
Relations to this entry
- bias-variance-decomposition← DEPENDS_ON
Bias-variance decomposition is defined in terms of Var(f̂) as a component of the expected squared error. Remove variance from the mathematical vocabulary and the decomposition cannot be expressed or evaluated operationally; the formula ceases to operate. Law 8b removal test satisfied.
Record identity
- Created
- Sep 4, 2026, 1:55 PM UTC
- Content hash
- 34a848fd949421fe289779dbaadc25a3d8a36efbd1ef0d74e5a2f81c9fa75b2a