Percentage Difference vs
Percentage Error

Percentage Difference

Percentage Difference has two meanings. This can lead to confusion!

On the page Percentage Difference we look at the common meaning when one is comparing an old value to a new value.

\|New Value - Old Value\|	× 100%

\|Old Value\|

(The "|" symbols mean absolute value, so negatives become positive)

Example: There were 200 customers yesterday, and 240 today:

\|240 - 200\|	× 100% = (40/200) × 100% = 20%

\|200\|

A 20% increase.

But if one value is not obviously the "old" value (for example we are comparing the heights of two people), then we should divide by the average of the two values:

\|Value1 - Value2\|	× 100%

(Value1 + Value2)/2

Example: "Best Shoes" gets 200 customers, and "Cheap Shoes" gets 240 customers:

\|240 - 200\|	× 100% = (40/220) × 100% = 18.18...%

(240+200)/2

The Percentage Difference between the two stores is about 18%

An interesting thing about this formula is that it doesn't matter which is "Value1" or "Value2"

Put the values the other way around:

\|200 - 240\|	× 100% = (40/220) × 100% = 18.18...%

(200+240)/2

The same answer, because we take the absolute value of |200-240| = 40

Percentage Error

The first formula is also called "Percentage Error", particularly when you know one value is exact:

\|Approximate Value - Exact Value\|	× 100%

\|Exact Value\|

Example: I thought 70 people would turn up to the concert, but in fact 80 did!

\|70 - 80\|	× 100% = (10/80) × 100% = 12.5%

\|80\|

I was in error by 12.5%

Percentage Difference vs Percentage Error