Scenario 3: The Doctor’s Scale

A patient visits their doctor for an annual checkup. At last year’s appointment their weight was recorded as 91 kg. This year it is recorded as 90 kg. The doctor notes in the chart: “Patient has lost 1 kg since last visit — positive trend, continue current plan.”

What the doctor does not mention: the clinic’s scale has an uncertainty of ±1.5 kg. This uncertainty comes from the way the scale rounds to the nearest 0.5 kg and from slight variations depending on how the patient stands on the scale.

A second scale in the clinic — a research-grade scale used for clinical trials — has an uncertainty of ±0.05 kg. The patient’s weight on that scale this year is (90.3 ± 0.05) kg. Last year’s weight on that scale was (90.8 ± 0.05) kg.

Discussion questions:

1. Given the uncertainty of the clinic scale (±1.5 kg), what is the range of possible true weights recorded last year? This year?
2. Do the two measurements from the clinic scale actually show a meaningful difference? Explain.
3. Now look at the research-grade scale data. Do those two measurements show a meaningful difference?
4. What does this scenario tell you about the relationship between instrumental precision and the claims you can make from your data?
5. The doctor made a confident clinical recommendation based on a 1 kg difference. Was that appropriate given the instrument being used?
6. Can you think of other everyday situations where the precision of a measuring instrument matters for a decision being made?