- State that measurement of any physical quantity is liable to uncertainty.
- Distinguish between random uncertainties and recognised systematic effects.
- State that the scale-reading uncertainty is a measure of how well an instrument scale can be read.
- Explain why repeated measurements of a physical quantity are desirable.
- Calculate the mean value of a number of measurements of the same physical quantity.
- State that this mean is the best estimate of a ‘true’ value of the quantity being measured.
- State that where a systematic effect is present the mean value of the measurements will be offset from a ‘true’ value of the physical quantity being measured.
- Calculate the approximate random uncertainty in the mean value of a set of measurements using the relationship: (maximum reading - minimum reading)/Number of readings.
- Estimate the scale-reading uncertainty incurred when using an analogue display and a digital display.
- Express uncertainties in absolute or percentage form.
- Identify, in an experiment where more than one physical quantity has been measured, the quantity with the largest percentage uncertainty.
- State that this percentage uncertainty is often a good estimate of the percentage uncertainty in the final numerical result of the experiment.
- Express the numerical result of an experiment in the form: final value ± uncertainty.

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Aids to Understanding

Reading scales.

Suppose you measure a piece of paper with the ruler below and you estimate it is a bit more than twenty two centimeters, say one fifth more.
The correct way to write your value is; 22.2 cm. Since the smallest scale division of the ruler is 0.5 cm the scale reading uncertainty is 0.25 cm , but we should
round it up (we never round uncertainties down) to 0.3 cm. The reading with uncertainty is written as

(22.2 +/- 0.3) cm. In meters we would write it as (0.222 +/- 0.003) m. It should now be clear that a ruler with 1.0 cm divisions we are justified in
taking our reading to three decimal places.
** Excercise **
Suppose a ball is dropped from a height of 3.3000 m five times. Suppose the times on the digital stopwatch were, 0.81 s, 0.92 s, 0.79 s 0.95 s and 0.99 s.

Your job is to write a report identical to the one on the right and find the average speed with its absolute uncertainty.