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1.7bFree

No formula? Measure it again and again instead

Your guide: Sir HamzaBelieves every formula has a story, and units never lie.

The problem

1.7a combined uncertainties from a formula. But a screw gauge measuring a wire's diameter has no formula at all — just six slightly different readings of the same wire. Where does the uncertainty come from now?

The answer is simple: measure it several times, average the readings, then look at how far each reading actually strayed from that average. That spread itself becomes the uncertainty.

Timing experiments use their own version of the same idea. Instead of repeating one instant, you count many vibrations at once, and the stopwatch's least count gets divided across all of them.

Find the average of several readings, then the mean deviation of each reading from that average. The mean deviation is the uncertainty in the average value. For timing, divide the stopwatch's least count by the number of vibrations counted.

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