What is the percentage difference between two numbers

General
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what is the percentage difference between two numbers

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What is the percentage difference between two numbers?

Answer: Calculating the percentage difference between two numbers is a useful way to understand the relative difference between them. Here’s a step-by-step guide on how to calculate the percentage difference:

1. Identify the Two Numbers:

Let’s denote the two numbers as ( A ) and ( B ).

2. Calculate the Difference:

Subtract the smaller number from the larger number to find the absolute difference.
\text{Difference} = |A - B|

3. Calculate the Average of the Two Numbers:

The average of ( A ) and ( B ) is calculated as:
\text{Average} = \frac{A + B}{2}

4. Calculate the Percentage Difference:

The percentage difference is then calculated using the formula:
\text{Percentage Difference} = \left( \frac{\text{Difference}}{\text{Average}} \right) \times 100

Example Calculation:

Let’s say we have two numbers, ( A = 150 ) and ( B = 100 ).

  1. Identify the Numbers:

    • ( A = 150 )
    • ( B = 100 )

  2. Calculate the Difference:
    \text{Difference} = |150 - 100| = 50

  3. Calculate the Average:
    \text{Average} = \frac{150 + 100}{2} = 125

  4. Calculate the Percentage Difference:
    \text{Percentage Difference} = \left( \frac{50}{125} \right) \times 100 = 40\%

Therefore, the percentage difference between the numbers 150 and 100 is 40%.

General Formula:

For any two numbers ( A ) and ( B ), the percentage difference can be expressed as:
\text{Percentage Difference} = \left( \frac{|A - B|}{\frac{A + B}{2}} \right) \times 100

This method ensures that the percentage difference is a measure of the relative difference between the two numbers, taking into account their average value.