# 2.2 Measurements and Data

## Accuracy

The accuracy of a measurement is how far away the measurement is from the true value, this can be expressed in literal terms however it can't then be compared to other measurements (e.g comparing literal accuracy of temperature measurement vs literal accuracy of micrometer). By dividing the difference by the actual value, the units cancel out and it can be compared to other measurements as a percentage. There is no quantifiable value at which a measurement becomes accurate as it depends heavily on context.

## Repeatability / Precision

This is a method of ensuring that the results weren't a fluke and can be obtained again with similar accuracy when using under the same conditions.

## Uncertainty

The uncertainty of a measurement is the interval within which a true value is expected to be. e.g if you measure the length of a piece of string using a ruler that is accurate to 1mm, if your measured value is 812mm then the actual value is $811.5 \le l < 812.5$.

The uncertainty can also be expressed in terms of standard deviations or another estimate for spread to account for random and systematic errors.

Absolute uncertainty is the literal value, with the string this would be $812 \pm 0.5; \text{mm}$

When plotting data, you draw the line of best fit of the measured data as well as the line of best fit for the worst fitting data (Using the error bars) in both directions to get a maximum and minimum gradient (Worst line of best fit). The uncertainty in the value of the gradient is then: $$\text{uncertainty} = \frac{1}{2}\times (\text{max gradient}-\text{min gradient})$$

## Percentage uncertainty

This can only be found when the real value is known (e.g calculating plancks constant) $$\text{p. uncertainty} = \frac{|\text{measured}-\text{real}|}{\text{real}}\times100%$$

As percentage uncertainty cancels out units it is irrelevant to the measured value and can be directly compared to other experiments (e.g you should always aim for a $1%$ uncertainty in your measurements)