Understanding the percent difference is a useful skill when you need to compare two numbers and determine the relative difference between them as a percentage. Unlike percentage change, which measures the change from an old value to a new value, percent difference provides a measure of difference between two numbers without implying a direction of change. This guide will explain how to find the percent difference, its formula, and when to use it.
Understanding Percent Difference
Percent difference is used to express the difference between two values as a percentage of their average. It’s particularly helpful when you are interested in the magnitude of the difference between two numbers, regardless of which number is larger or smaller. This is different from percentage change, where the order of values matters significantly.
For instance, if you are comparing the price of a product at two different stores, you might want to know the percent difference to understand how much prices vary, without necessarily focusing on which store is “changing” its price relative to the other.
The Formula for Percent Difference
The formula to calculate the percent difference is as follows:
( text{Percent Difference} = dfrac{|V_1 – V_2|}{left[dfrac{(V_1 + V_2)}{2}right]} times 100 )
Where:
- ( V_1 ) is the first value.
- ( V_2 ) is the second value.
- ( |V_1 – V_2| ) is the absolute value of the difference between the two values. This ensures the difference is always positive, as we are concerned with the magnitude of the difference.
- ( dfrac{(V_1 + V_2)}{2} ) is the average of the two values. Using the average as the denominator provides a neutral base for comparison.
Steps to Calculate Percent Difference
To calculate the percent difference, follow these simple steps:
- Find the difference between the two numbers. Subtract one value from the other. Since we use the absolute value, the order doesn’t matter.
- Calculate the average of the two numbers. Add the two numbers together and divide by 2.
- Divide the difference by the average. This gives you the difference as a decimal.
- Multiply by 100 to express as a percentage.
- Append the percent sign (%) to your result.
Example Calculation: Percent Difference Between 5 and 7
Let’s calculate the percent difference between 5 and 7 using the formula.
Let ( V_1 = 5 ) and ( V_2 = 7 ).
- Find the difference: ( |5 – 7| = |-2| = 2 )
- Calculate the average: ( dfrac{(5 + 7)}{2} = dfrac{12}{2} = 6 )
- Divide the difference by the average: ( dfrac{2}{6} = 0.333 )
- Multiply by 100: ( 0.333 times 100 = 33.33 )
- Add the percent sign: ( 33.33% )
Therefore, the percent difference between 5 and 7 is 33.33%.
Percent Difference vs. Percent Change
It is important to distinguish between percent difference and percent change.
- Percent Difference: Measures the relative difference between two numbers. The order of numbers does not matter. It’s used when you want to know how different two numbers are from each other, without focusing on an increase or decrease from a starting point.
- Percent Change: Measures the change from an old value to a new value. The order is crucial. It’s used to track the relative change over time or between conditions, indicating an increase or decrease from a baseline. To calculate percentage change, you would use a different formula focusing on the change relative to the original value.
In summary, if you need to quantify the disparity between two numbers symmetrically, percent difference is the appropriate measure. If you are tracking change from one value to another, use percentage change instead.
