Three archers each fire four arrows at a target. Joe’s four arrows hit at points 10 cm above, 10 cm below, 10 cm to the left, and 10 cm to the right of the centre of the target. All four of Moe’s arrows hit within 1 cm of a point 20 cm from the centre, and Flo’s four arrows hit within 1 cm of the centre. The contest judge says that one of the archers is precise but not accurate, another archer is accurate but not precise, and the third archer is both accurate and precise. Which description applies to which archer? Explain.

The archer holds the feathered end of the arrow against the string and pulls it back.

Releasing the string throws the arrow forward with the elastic force of the bow.

Joe is accurate because all his arrows landed 10 cm from the center (which can be considered within tolerance), but they are not accurate because they did not land in the same place (they ended up in all directions).

Hence, Joe is accurate but not precise.

Moe is not accurate as his arrows landed far from the intended target (20 cm) but is precise because all the arrows ended up nearby (within 1 cm).

Hence, Moe is precise but not accurate.

Flo is both accurate (as his arrows landed near the centre) and precise (all arrows landed with in 1 cm of the centre).

Hence, Flo is accurate and precise.