Compare Rates with Matching Denominators

Supplied materials

• Original fictional archive-box check: Box A contains 20 recorded items; 5 have a supplied date. Box B contains 40 recorded items; 8 have a supplied date. Count each item once, and use all recorded items in its own box as the denominator. No missing boxes are described.

Learn the idea

A total and a proportion can rank groups differently. Box B has more dated items in absolute number, eight compared with five. But the dated share depends on the total number of items in each box. Keep the numerator’s meaning and denominator’s scope consistent before comparing percentages.

A rate answers a particular question. “Which box has more dated items?” compares counts. “Which has a larger dated share?” compares fractions. Neither measurement tells us whether the items are accurate, important, or typical of an entire archive. These judgments would require additional evidence beyond a date label and an item count.

1. Write each dated count over its box total.
2. Convert 5/20 and 8/40 to percentages.
3. Answer the count question and the share question separately.
4. Write one historical question these proportions cannot answer.

Check your reasoning

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Take it further

Changed Box B: ten of its forty items are dated. Model reasoning: “B’s share becomes 10/40=25%, equal to A’s. B still has more dated items, ten versus five; equal shares do not require equal counts when denominators differ.”

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