Tables, graphs, repeated measurements and evidence quality

Keep the observations before summarising them

A useful table identifies the sample or object, sequence or time, quantity, unit and relevant conditions. For the two constructed sets here, the full record is: run 1, set A 49.8 mm and set B 49.7 mm; run 2, A 50.0 mm and B 49.9 mm; run 3, A 50.2 mm and B 50.1 mm; run 4, A 50.0 mm and B 50.3 mm. These are repeated readings of an assumed unchanged object, not four different parts.

Store the instrument indications as recorded. Put corrections and calculations in separate fields. A missing reading is not zero. If a point is excluded because the instrument slipped, retain it with the reason and show how inclusion affects the conclusion. Quietly deleting inconvenient results makes later review impossible.

Choose axes that answer the question

A run-sequence graph puts reading order on the horizontal axis and the measured value on the vertical axis. It can expose drift, a sudden change or unusual variation. The diagram plots the complete sets from the table. Circles with a solid line identify A; triangles with a dashed line identify B, so colour is not the only distinction. The connecting lines show sequence, not measured values between readings.

The vertical axis spans 49.6 mm to 50.4 mm rather than starting at zero. This makes small changes legible, and the explicit limits prevent that magnification from being hidden. A bar chart of absolute lengths on the same shortened axis could exaggerate a size comparison. Select a display that suits the question and disclose any restricted scale.

To study response to an input, plot the actual input quantity with units rather than an arbitrary reading number. Mark distinct experimental conditions and explain what uncertainty bars mean. An attractive line through points is not evidence of a physical law; its model and the data supporting it need examination.

Decide what repetition can tell you

Repeated measurements help characterise variation. If observations are independent and the process is stable, averaging can reduce the standard uncertainty associated with random variation in the mean. Repeatedly copying one displayed value or sampling faster than the system changes does not create independent evidence. Shared calibration effects also remain.

Four rising readings suggest a question; they do not prove a cause. The object may be warming, the instrument may drift, or the setup may change. Record temperature and timing, inspect the setup and plan an appropriate check. A sample mean is a description of these observations, not automatically a trustworthy estimate for all later conditions.

Match the claim to the sampling

Repeated readings of one object answer a different question from measurements of four independently chosen objects. The first explores the measurement procedure; the second may explore variation in production, with measurement variation mixed in. A carefully measured convenient sample can still miss other sizes, users or operating conditions.

Evidence quality depends on a defined question, appropriate sampling, a suitable procedure, recorded conditions and an honest account of uncertainty. More rows do not compensate for consistently measuring the wrong property. State which population or operating range the data can reasonably support.

Compare summaries with the full sequence

Set A sums to 200.0 mm, so its mean is 200.0/4 = 50.0 mm. Its range, maximum minus minimum, is 50.2 − 49.8 = 0.4 mm. Set B also sums to 200.0 mm and has the same mean, but its range is 50.3 − 49.7 = 0.6 mm.

The means alone conceal the larger range and rising sequence in B. The range is a simple description of these four readings, not a complete uncertainty evaluation. Before combining B into a final result, investigate whether the assumption of unchanged conditions is reasonable.

Try the reasoning

1. Why retain reading order when the final report includes an average?

   Show the answer and reasoning

   Order can expose drift or shifts that the average hides. A sequence plot helps test whether combining the readings is sensible.

2. Do ten readings of one part establish how much a batch of ten parts varies?

   Show the answer and reasoning

   No. They mainly inform repeatability on that part. Batch variation needs an appropriate sample of different parts and attention to measurement variation.

3. A graph starts at 49.6 mm. Is that automatically misleading?

   Show the answer and reasoning

   No. A clearly labelled restricted axis can reveal small changes. The display must suit the question and make the restricted scale obvious.

What to carry forward

Keep raw observations and their order, show units and honest scales, and make claims no broader than the measurement and sampling support.