Data sampled from groups with σ2 = 0.9

This diagram illustrates the formula for the pooled estimate of the common variance,

The numerator for the pooled estimate is the sum of the squared lengths of all coloured vertical lines.

Explain that when all group sizes are equal, the pooled estimate is simply the average of those within the three groups.

Use the pop-up menu to display data with different numbers in the groups and mention that the variance in the biggest group gets the highest weight in the formula.

Mention that the formula is valid even if some groups only have a single observation.