Uses and Abuses of Percentages 3a

Flashcards about using and understanding percentages.

Give three ways of using percentages.

As fractions, to describe change, and for comparisons.

How to calculate the number of people who said the President is doing a good job if 35% of 1069 people surveyed said so?

Multiply 0.35 by 1069, which equals approximately 374 people.

What is the formula for absolute change?

new value – reference value

What is the formula for relative change?

Absolute change / reference value

What is the absolute change in stock price if it doubled from $7 to $14?

$7

What is the relative change in stock price if it doubled from $7 to $14?

100%

What is the formula for absolute difference?

compared value – reference value

What is the formula for relative difference?

Absolute difference / reference value

If a new value is P% more than the reference value, what percentage of the reference value is it?

(100 + P)%

If a new value is P% less than the reference value, what percentage of the reference value is it?

(100 - P)%

If Jada earns 200% more than Reggie, how many times as large as Reggie’s income is Jada’s?

3 times as much

If a bank increases its interest rate from 3% to 4%, by how many percentage points did the interest rate increase?

1 percentage point

If the compared value is P% more than the reference value, what is the formula to calculate the compared value?

compared value = (100 + P)% × reference value

Why is it important to beware of shifting reference values when discussing percentages?

Because it can lead to misleading conclusions, such as a stockbroker claiming a 15% gain after a 60% loss followed by a 75% gain.

Why can't percentages always be averaged?

Because the reference values may be different, leading to an inaccurate overall percentage (e.g., batting averages).