# Calculating difference of percentages

Sometimes, in research articles the difference between two percentage is reported directly. How is it right? Example:

State A has 75% of people of X kind. State B has 80% of people of X kind.

The difference is generally reported as... The difference in these two states (A,B) in terms of people of kind X is only 5 %.

Should we not calculate the percentage difference as follows?

100*(80-75)/80 = 6.25%


Or why not it is

100*(80-75)/75 = 6.66%

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I am surprised that research articles (news media I could understand) are written in this manner as it seems quite meaningless. Suppose State A has 100 people in total all of kind X (ie, 100%), and State B has 1,000,000 people where 500,000 are of type X (ie 50%), than what does it tell you by saying that "the difference between State A and State B is 50%"? – Peter Grill Mar 30 '12 at 1:17
With the difference between State A and State B is 50% I meant to contrast these two States. I know dividing by 80 or 75 is not correct but how can we just take the difference between unrelated (difference base) percentages. I guess it is a crude way of reporting differences. – Stat-R Mar 30 '12 at 12:20
It is, but that's what's meant. What would be more meaningful would be to report the overall percentage of people of type $X$. The $5\%$ does have some meaning, though. It gives you a sense of how different being in one state is from being in another. It just doesn't give you a good feel for how these statistics might play out at an interstate level. – Brett Frankel Mar 30 '12 at 15:45

There's no reason to divide by $80$ or $75$ as you did above.
$80\%=0.80$ and $75\%=0.75$.
$0.80-0.75=0.05=5\%$