File:Scaled chi squared.svg

English: A plot of the scaled chi-squared probability distribution, the probability distribution of the sample variance s²,

${\displaystyle s^{2}={\frac {\;\sigma ^{2}}{\nu }}\;\chi _{\nu }^{2}}$

where s² is the mean of the squares of ν independent normal distributions of mean 0 and standard deviation σ; plotted here for the case σ = 1.0.

Equivalently this is also a plot of the distribution of the variance ratio s²/σ² for any value of σ. As ν increases s²/σ² becomes more sharply peaked close to 1