Grade 10 · lesson 2 of 4

Audit a Change in Measurement

Determine whether before-and-after figures use the same definition.

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Supplied materials

  • Complete original fictional museum record: In 1951, a clerk counted 200 unique visitors in a month using one numbered card per person. In 1953, an automatic counter recorded 260 entries in a month, including repeated visits. A bus service began in 1952. No 1953 unique-person count or 1951 entry count is supplied. These dates describe an invented museum, not real history.

Learn the idea

A before-and-after comparison requires matching quantities. A unique-visitor count and an entry count are not the same measure, even when both are labeled “visits” in a later summary. Write each operational definition: what was counted, how often a person could count, and the period covered. Consistent units alone do not guarantee consistent meaning.

The numerical difference is sixty, but it cannot be interpreted as sixty additional unique visitors from these records. Repeat entries could produce some or all of that gap, and true attendance could also change. The bus occurred between the dates, yet inconsistent measures block even the simple growth claim needed before evaluating a bus effect.

  1. Label the 1951 and 1953 measures as unique people or entries.
  2. Record whether repeat appearances count again.
  3. Calculate the numerical difference while qualifying what it means.
  4. Specify a same-period crosswalk count that would let both measures be compared.
Worked example

See the method in action

“260−200=60 is a difference between entry and unique-person figures, not established visitor growth. For 1953, counting unique people alongside entries could show the repeat-entry gap; comparable unique-person totals in both periods would support a growth comparison, though not isolate a bus cause.”

Your turn

Check your reasoning

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Which conclusion is justified?

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See the answer and explanation

The records use different measures, so they do not establish a sixty-person increase.

One count permits repeats and the other does not. The difference is computable as numbers but does not establish change in one consistent quantity.

Take it further

Changed input: a matched 1953 unique-person count is added: 230. Model reasoning: “Comparable unique-person counts now show 230−200=30 additional unique visitors across the periods. The 260 entries also imply 30 entries beyond one per unique person in 1953. Neither calculation alone assigns a causal bus effect.”

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