Working with percentages is like walking a minefield
By MUNGAI KIHANYA
The Sunday Nation
Nairobi,
10 September 2006
It is amazing how easily people get entangled when
quoting figures in percentages. May be this is because most individuals
do not take a moment to think about the meaning of their statements.
Consider this example:
A recent news report stated that the allowances for
government officials attending conferences had been “reduced by as much
as 500 percent”. Now, what does that mean? Suppose the officers were
getting Sh100. What is 500 percent of Sh100? The answer is Sh500.
Therefore, if the allowance is REDUCED by 500 percent, then Sh500 will
be taken away from the initial Sh100. The resulting payment is negative
Sh400. But a negative pay can only mean that the officers would give
Sh400 to the government when they attend a conference! That would be
ridiculous.
Reading the story farther, it turns out that the
allowances have actually been reduced from Sh5,000 to Sh1,000. The
question then is: What was the percentage reduction? Let us calculate
it…slowly. The initial payment was Sh5,000. The new figure is Sh1,000.
Therefore the reduction is Sh4,000. Now, what percentage (of Sh5,000) is
Sh4,000?
To get the answer, we simply divide 4,000 by 5,000
and multiply the result by 100. The result is 80. Thus the reporter
should have said that allowances have been reduced by 80 percent; not
500 percent. But why did the write get confused?
I guess he reasoned that increasing from Sh1,000
to Sh5,000 is a 500 percent rise
and concluded that if you do the reverse, the reduction must also be 500
percent. Unfortunately, that kind of reasoning is faulty on two counts.
First of all, a rise from Sh1,000 to Sh5,000 is NOT equivalent to a 500
percent increase. Think about it: the change is Sh4,000 and that is
equal to 400 percent of Sh1,000.
The second fault arises from the fact that if you
increase a number by a certain percentage and then reduce the result by
the exact same fraction, you do NOT get back to the original value. That
might sound weird but here is a simple proof:
If we increase 100 by 20 percent, we get 120.
Reducing 120 by 20 percent gives 96 (20 percent of 120 is 24; 120 minus
24 is 96). The reverse is also true: if you reduce a figure by a certain
percentage and the increase it by the same fraction, you do NOT get back
where you started. Try it for yourself and see.
***
Several readers have asked me to comment on the
trillion shillings investment expected at the coast. Now that is a lot
of money in any currency, equal to about 15 billion dollars. What I find
most intriguing is that when I searched for “Al Bader International”
(the company that is to make this investment) on the internet
(www.google.com), I found only 50 results – and all had something to do
with the story carried the Nation. The name of its chairman (“Yousef Abdul Aziz Al Bader”)
yielded only six results. In comparison, a search for “
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