# 10.03 Using the furthest edge of the uncertainty interval

Consider the same three examples but this time taking the error to be between the true value (the bullseye in this analogy) and the furthest limit of the uncertainty interval (the outer perimeter of the grouping in this analogy). This will produce more sensible conclusions and also illustrate the way that precision affects accuracy

## Example 1

Marksman A produces a grouping 5cm in radius, the centre of this grouping lies 1cm from the bullseye. None of the individual bullet holes are closer than 3.5cm from the bullseye.
Marksman B produces a grouping of radius 1cm whose centre is 1.2cm from the bullseye.
Marksman B is more accurate because their furthest shot lies just 2.2cm from the bullseye compared to 6cm for marksman A.
All of the shots of Marksman B are closer to the bullseye than any of Marksman A's

A measurement of 9.9 +/- 0.2cm is more accurate than 10 +/- 0.5 cm for a true value of 10.1cm because the errors are 0.4 cm and 0.6 cm respectively

## Example 2

Marksman A produces a grouping 5cm in radius, the centre of this grouping lies 1cm from the bullseye. None of the individual bullet holes are closer than 3.5cm from the bullseye.
Marksman B produces a grouping of radius 1cm whose centre is 1cm from the bullseye.
Marksman B is more accurate because their furthest shot lies just 2cm from the bullseye compared to 6cm for marksman A.
All of the shots of Marksman B are closer to the bullseye than any of Marksman A's

A measurement of 10 +/- 0.2cm is more accurate than 10 +/- 0.5 cm for a true value of 10.1cm because the errors are 0.3cm and 0.6cm respectively

## Example 3

Marksman A produces a grouping 5cm in radius, the centre of this grouping lies dead on the bullseye. However none of the individual bullet holes are closer than 4.5cm from the bullseye.
Marksman A is still not very accurate because his furthest shot is still 5cm from the bullseye and even his closest shot is 4.5cm away.

A measurement such as 10 +/- 0.5 cm for a true value of 10cm is not completely accurate because there is still an error present of 0.5cm due to the width of the uncertainty interval!