Data & Statistics at the 700-800 Level

This topic is reading two-way tables and drawing rates out of them. The arithmetic is division. The difficulty is entirely in choosing the denominator, and every hard item is engineered so the wrong denominators are also available as answers.

The denominator decides. A single cell supports three completely different percentages depending on whether you divide by the grand total, the row total, or the column total. The rule: the phrase immediately after 'of' names the group you have been restricted to, and that group's total is your denominator. Circle it before you divide.

Rate comparison across rows asks which group has the greatest proportion, which is rarely the group with the greatest count — the largest group almost always supplies the largest raw count, and that is the trap. Scaling a sample to a population obeys one rule: the rate's denominator must match the population you are scaling. Estimating over the whole population requires a whole-sample rate; estimating within a subgroup requires a rate computed inside that row. Mixing them is the signature error, and the item is built so the mismatch produces a plausible number.

When a stated rate is to be applied to a new or regrouped population, use the rate belonging to the group the stem names — not the overall rate.