Work out chi square distribution instantly with clear inputs, formula shown and shareable results.
The chi-square distribution is the sum of squares of independent standard normals, with mean equal to its degrees of freedom and variance twice that. It underpins goodness-of-fit and variance tests.
Chi-square CDF
P(X ≤ x) = P(df/2, x/2), the regularised lower incomplete gamma
11.07, so a statistic of exactly that gives a p value of 0.05.
Squares are non-negative and occasionally large, so the distribution has a long right tail that shortens as df grows.