Expressing Percentages

Date: 01/26/2004 at 04:15:23
From: YrbkMgr
Subject: Different Ways to Express Percentages

Why do we sometimes use phrases like "4 out of 5 dentists" or "1 in 3 
people"? Is there any value in using expressions like that over 
straight percentages?

It seems to me that it's far easier to understand if we say 80%
instead of 4 out of 5, or 33% instead of 1 in 3.  As far as I can see, 
one has to convert it to percentages anyway to be meaningful--doesn't one?

Date: 01/26/2004 at 09:41:35
From: Doctor Ian
Subject: Re: Different Ways to Express Percentages

Hi,

If you're comfortable with percentages, a straight percentage is
easier to understand.  However, many people are not comfortable with
percentages.  

As a rule of thumb, people are comfortable with small numbers.  Saying
"4 out of 5 dentists" is an easy thing to visualize:  think of 5
dentists, representing all the dentists in the country (or the world),
and imagine one of them standing off by himself.  Now try the same
thing with 100 dentists, separated into groups of 80 and 20. 

Note that neither representation is more meaningful than the other. 
They're both normalized ratios, telling us nothing about how many
dentists were actually consulted.  

If we ask 20 dentists for an opinion, and 16 of them say one thing,
while the remaining 4 say something else, "4 out of 5" communicates
the ratio with the smallest integral denominator; and 80% communicates
the ratio with the somewhat arbitrary denominator of 100.  

The main reason for using percentages instead of integer ratios is
that they're easy to compare.  Comparing "3 out of 8" to "2 out of 5"
isn't easy for most people; but comparing "38%" to "40%" is a snap.

Does this help?

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/