The Chi-Square Distribution

Statistics · Axiom Academy

INTRO The Chi-Square Distribution Discover how squaring normal values creates a powerful new distribution. Start by drawing a random value from a standard normal distribution and squaring it. Watch what happens! Generate many squared normal values and watch the distribution emerge. See the characteristic right-skewed shape! ➕ Step 3: Sum of Squared Normals Now add together multiple independent squared normal values. This is where degrees of freedom come in! Step 4: How Shape Changes with df Explore how the chi-square distribution transforms as degrees of freedom increase. Notice the dramatic changes! The chi-square distribution with k degrees of freedom is the sum of k independent squared standard normal variables: Range: Only non-negative values (0 to ∞) Mean: μ = k Variance: σ² = 2k Shape: Right-skewed, becomes more symmetric as k increases The chi-square distribution is fundamental in statistics for goodness-of-fit tests, tests of independence, and constructing confidence intervals for variance.

This is the written version of the interactive lesson above. See the full Statistics course.