Percentage of Increase/Decrease: If a regular haircut costs $5.00 in 1965...

KWF

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If a regular haircut costs $5.00 in 1965, and now approximately 50 years later the same haircut costs $20.00, is this increase a 200% increase or a 300% increase?

Which calculation should be used to determine the correct percentage?

1. ($20.00 - $5.00)/$5.00 = $15.00/$5.00 = 3 = 300% or expressed as $5.00 + (300% * $5.00) = $20

2. $20.00/$5.00 = 4 = 400%; 400% * $5.00 = $20.00
 
If a regular haircut costs $5.00 in 1965, and now approximately 50 years later the same haircut costs $20.00, is this increase a 200% increase or a 300% increase? Which calculation should be used to determine the correct percentage?
1. ($20.00 - $5.00)/$5.00 = $15.00/$5.00 = 3 = 300% or expressed as $5.00 + (300% * $5.00) = $20
2. $20.00/$5.00 = 4 = 400%; 400% * $5.00 = $20.00
Suppose the \(\displaystyle NP\) stands for new price & \(\displaystyle OP\) stands for old price.
Then the percent of increase/decrease is \(\displaystyle \dfrac{NP-OP}{OP}\).
 
If a regular haircut costs $5.00 in 1965, and now approximately 50 years later the same haircut costs $20.00, is this increase a 200% increase or a 300% increase?

Which calculation should be used to determine the correct percentage?

1. ($20.00 - $5.00)/$5.00 = $15.00/$5.00 = 3 = 300% or expressed as $5.00 + (300% * $5.00) = $20

2. $20.00/$5.00 = 4 = 400%; 400% * $5.00 = $20.00
What you are asking is about linguistic usage.

If the average price of a haircut was $5 and $20 in 1965 and 2015 respectively, it is obvious that the later price is four times the earlier price. No one disputes that.

It is also clear in that case that the actual increase in the average price of a haircut is $15.

But for many purposes, we want to compare relative increases. Suppose over the same period the average price of a manicure increased from $60 to $75. That is also an actual increase of $15. But 75 is not four times times 60. And suppose the average price of a bunch of bananas went from $1 to $4. That is an actual increase of only $3, not $15, yet the later price is 4 times the earlier.

In fact, it is so common to refer to relative change that we frequently leave off the word "relative," which can lead to confusion.

How do measure the actual change?

We subtract the earlier price from the later price. In the haircut case, where the price went from $5 to $20, the change is 20 - 5 = 15. The increase does not include the original price. No one would say that the price increased by $20 if it went from $5 to $20.

The same principal applies to measuring relative change. We divide the difference in prices by the original price to figure out what the change is relative to the original.

\(\displaystyle \dfrac{20 - 5}{5} = \dfrac{15}{5} = 300\% = \text { relative change in average price of haircut.}\)

\(\displaystyle \dfrac{75 - 60}{60} = \dfrac{15}{60} = 25\% = \text { relative change in average price of manicure.}\)original.

\(\displaystyle \dfrac{4 - 1}{1} = \dfrac{3}{1} = 300\% = \text { relative change in average price of bananas.}\)
 
… Which calculation should be used to determine the correct percentage?

1. ($20.00 - $5.00)/$5.00 = 3 = 300%

2. $20.00/$5.00 = 4 = 400%
The first one.

It matches the percent-change formula, described by pka in post #2:

(NEW minus OLD) divided by OLD

A positive result represents a 'percent increase', and a negative result represents a 'percent decrease'.


PS: As Jeff mentioned, people get sloppy with their descriptions. That ought to be something like, "percent change"or "relative percentage difference", to be clear. :cool:
 
The first one.

It matches the percent-change formula, described by pka in post #2:

(NEW minus OLD) divided by OLD

A positive result represents a 'percent increase', and a negative result represents a 'percent decrease'.


PS: As Jeff mentioned, people get sloppy with their descriptions. That ought to be something like, "percent change"or "relative percentage difference", to be clear. :cool:


What type of situation would calculation 2. be used in, $20.00/$5.00 = 4 = 400%?
 
What type of situation would calculation 2. be used in, $20.00/$5.00 = 4 = 400%?

That tells you what percentage of the original the new price is. In this case, 400% of $5 is $20. That's the same as "4 times as much".
 
That tells you what percentage of the original the new price is. In this case, 400% of $5 is $20. That's the same as "4 times as much".

If I understand correctly, is it correct to indicate that the $5.00 price of the haircut increased 300% and also that the current price ($20.00) is 400% of the $5.00 price or 4 times the $5.00 price. (?)

It can be expressed both ways.
 
If I understand correctly, is it correct to indicate that the $5.00 price of the haircut increased 300% and also that the current price ($20.00) is 400% of the $5.00 price or 4 times the $5.00 price. (?)

It can be expressed both ways.

Correct.
 
If I understand correctly, is it correct to indicate that the $5.00 price of the haircut increased 300% and also that the current price ($20.00) is 400% of the $5.00 price or 4 times the $5.00 price.
The % of increase/decrease in price is \(\displaystyle \dfrac{NP-OP}{OP}=\dfrac{20-5}{5}=3\) or \(\displaystyle 300\%\).
 
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