Match Conclusions to Measurement Limits

Use ranges, overlap, and measurement precision responsibly.

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A mean summarizes repeated values but hides their spread. Check ranges for overlap. Avoid claiming a tiny difference is reliable when measurements are coarse or trials are few.

Worked example

Times of 10, 12, and 11 seconds have mean 11 and range 10 to 12. Another mean of 11 alone does not tell you whether its individual times varied more.

Rolling Cart Test

A class timed the same cart on two tracks of equal length. Times were recorded to the nearest whole second. Track A: 8, 10, 9 seconds. Track B: 9, 9, 9 seconds. Both means are 9 seconds. The class completed only three trials on each track.

1. What are the lowest and highest recorded times for Track A? 9 to 9 seconds 8 to 10 seconds 8 to 27 seconds

2. Which track has less variation in its recorded times? Track A Neither can be compared at all Track B

3. What comparison of means is supported? The recorded means are equal A's mean is smaller B's mean is smaller

4. Does recording every B trial as 9 seconds prove the exact times were identical? Yes, rounding preserves every detail No, whole-second rounding can hide small differences Yes, three trials prove all future times

5. What would strengthen a follow-up comparison? Using different carts and lengths Keeping only the fastest trial More trials with finer time measurements

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