UNIT 3A: Uses and Abuses of Percentages

abuses of percentages

-Beware of shifting reference values -Less than nothing -Don't average percentages

three ways to write percentages

-as fractions -to describe change -for comparisons

Less than nothing

Decrease caloric intake by 150% to lose weight (not possible) *cannot decrease by more than 100%.

Don't average percentages

If 70% of the boys and 60% of the girls in a class voted to go to a water park, then 65% of the students in the class voted to go to the park.

relative change

a fraction that describes the size of absolute change in comparison to the reference value [relative change = (absolute change)/(reference value) = (new value-reference value)/(reference value) × 100%]

When a change or difference is expressed in percentage points

absolute change

absolute change

an actual increase or decrease from a reference value (starting number) to a new value [absolute change = new value - reference value]

If the compared value is P% more than the reference value

it is (100+P)% of the reference value.

If the compared value is P% less than the reference value

it is (100-P)% of the reference value.

If the compared value is P% of the reference value

it is P/100 (or %) times the reference value.

Of means

multiply (also can be represented by 'times')

percent

per 100, or divide by 100

When a change or difference is expressed with % sign or word percent

relative change or difference

than means

start with the something

More than means

start with the something and add to it. Ex: 20% more than means 100% of original + 20% more = 120%

Less than means

start with the something and subtract from it (important to subtract in correct order). Ex: 20% less than means 100% original - 20% = 80% of original

absolute difference

the actual difference between compared value and reference value [absolute difference = compared value - reference value]

relative difference

the description of the size of the absolute difference as a fraction of the reference value [relative difference = (absolute difference)/(reference value) = (compared value-reference value)/(reference value) × 100%]