Shop prices and GST

Comparing percentages Percentages put different-sized groups on a common scale. For each group, divide by its own total. If the question asks how much more or less A is than B, B is the reference for that comparison. Example A team wins 8 of 10 games. Another wins 12 of 20. Their win rates are 810 x 100%=80% and 1220 x 100%=60%. The first team has the higher win rate although it won fewer games. The difference between the numbers of wins is 4. Relative to 8 wins this is 48 x 100%=50%; relative to 12 wins this is 412 x 100%=33 13%. Changing the reference changes the relative comparison. Check which question you answered: highest count, highest share of a total, or size of a gap relative to one quantity.

Percentages put different-sized groups on a common scale. For each group, divide by its own total. If the question asks how much more or less A is than B, B is the reference for that comparison.

A team wins 8 of 10 games. Another wins 12 of 20. Their win rates are \(\dfrac{8}{10}\times100\%=80\%\) and \(\dfrac{12}{20}\times100\%=60\%\). The first team has the higher win rate although it won fewer games.

The difference between the numbers of wins is 4. Relative to 8 wins this is \(\dfrac{4}{8}\times100\%=50\%\); relative to 12 wins this is \(\dfrac{4}{12}\times100\%=33\dfrac{1}{3}\%\). Changing the reference changes the relative comparison.

Check which question you answered: highest count, highest share of a total, or size of a gap relative to one quantity.