Appendix E:Percentage Points 
of the Chi-Square Distribution
Let X1, … , Xn be a random sample from a normal distribution with mean μ and variance σ2, and let S2 be the sample variance. Then the random variable
has a chi-square (χ2) distribution with n − 1 degrees of freedom.
The probability density function of a χ2 random variable is
where k is the number of degrees of freedom. The mean and variance of the χ2 distribution are k and 2k, respectively. The limiting form of χ2 distribution as k → ∞ is the normal distribution.
The percentage points of the χ2 distribution are given in the following table. We define 
as the percent point or value of the chi-square random variable with ν degrees of freedom such that the probability that χ2 exceeds this value is α. We can write it as
The χ2 distribution is skewed, and hence we need to find separate value for 
from the table.
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