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Percent Change, Increase, Difference

Date: 07/15/97 at 08:24:03
From: Allistair
Subject: Percent difference

I haven't had math in years and I need a little help here. Say you 
have two numbers 5 and 7. You want to know what is the difference in 
percent between the two numbers.

Below is an real example of the problem I'm working on.

1991 = $2346.80

1992 = $3608.29

Percent change 91-92 = ?

Date: 07/15/97 at 09:02:14
From: Doctor Rob
Subject: Re: Percent difference

First you need to compute the difference between the two amounts. 
Then you make a fraction of that difference over the first of the two 
amounts. Finally you convert the fraction to a percentage by dividing 
the denominator into 100 times the numerator.

In your example, dropping the dollar signs, the difference is
3608.29 - 2346.80 = 1261.49. The fraction is 1261.49/2346.80, and the 
percentage comes from dividing 2346.80 into 126149. The result is 
53.75, and since the sign is positive, this is a 53.75 percent 
increase from 1991 to 1992.

In the other example, 5 and 7, the difference is 2, the fraction is 
2/5, and the percentage is 5 divided into 200, or 40. Thus 7 is
40 percent larger than 5.

On the other hand, if you take 7 and 5, the difference is -2, the
fraction is -2/7, and the percentage is 7 divided into -200, or
-28.57. Thus 5 is 28.57 percent smaller than 7.

It may seem paradoxical that if we start with 5 and add 40 percent, we 
get 7, but to get back to 5 we have to subtract only 28.57 percent.  
The reason these percentages are different is that they are 
percentages of different amounts: 40 percent of 5, and 28.57 percent 
of 7 - both are equal to 2.

For more about percentages and fractions, see the Dr. Math FAQ:   

-Doctor Rob,  The Math Forum
 Check out our web site!   

Date: 05/05/2003 at 18:01:25
From: Jerone Anderson
Subject: Percent difference

The above explanation defines percent difference as ((q1-q2)/q2)*100, 
which is used in many calculations for percent error rather than 
percent difference. Percent difference is defined as 
(|q1-12|/((1/2)*(q1+q2)))*100 for comparing values.

I am confused, as the terms percent difference and percent error are 
not consistent with what is expected in many classes.

Date: 05/05/2003 at 22:57:56
From: Doctor Peterson
Subject: Re: Percent difference 

Hi, Jerone.

The above is really about "percent change" or "percent increase," 
rather than "percent difference," since there is an "old" and a "new" 
value. In that case, you take the percentage of the old value.

When there is no directionality to the difference, so you can't 
distinguish an "old" value from a "new" value, you have to use the 
average of the two as the standard of comparison, as in your formula.

This is one of many cases where terms are used differently in various 
contexts, and what is a minor error of terminology in one question can 
lead to major confusion for people coming at it from a different 

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum      
Associated Topics:
Middle School Fractions

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