More Than 100%
I am trying to understand percentages. I
understand that it is a formula such as the part/whole x 100
gives me a percent answer, but if 100% is the whole value, how
can I get 300%? Is this considered the percent change from the
original value or would it be better explained as three times the
You raise an important issue that is flagrant in both scientific
and non-scientific literature. It is absolutely necessary when
expressing percentages, to specify the percentage of WHAT!!
Example: If a salt doubles its solubility if the temperature is
raised from 25C to 50C it is OK to say the solubility increases by
200% = 2 x 100/%, but without specifying that the basis of the
percentage is the solubility at 25C., the 200% has no meaning.
Unfortunately, in socially charged issues protagonists and
antagonists often toss out percentages without specifying the basis
of the percentage.
An intentionally skewed example: "The population of the US has
increased by 1000%." But what is the present population compared to
-- the last census, or the estimated population in 1800?
I refer you to the classic book "How to Lie with Statistics" by
Darrell Huff for more subtle examples of the misuse of numbers.
100% means the whole value of reference. You cannot just have 100%. You
must have 100% of something, or more often 100% of an amount. Less than
100% is less than that amount. More than 100% is more than that amount.
300% of $15.00 is (300/100)*($15.00)=$45.00. You cannot receive 300% of the
$15.00 from the wallet that holds that original $15.00, but you can get it
from a different source. You can get it from a bet at the racetrack. Odds
of 3-to-1 mean that if you win, you will get 300% of the original bet as
winnings. Of course, you will also get back your original bet money.
Dr. Ken Mellendorf
Illinois Central College
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Update: June 2012