Mathematical Formula For Calculating Percentage Difference
\[ \text{Percentage Difference} = \frac{\left| \text{Value 1} – \text{Value 2} \right|}{\frac{\text{Value 1} + \text{Value 2}}{2}} \times 100 \]
Example Broken Down With Steps
$$
\text{Given: Value 1 = 80, Value 2 = 100}
$$
$$
\text{Step 1: Subtract smaller value from larger value: } 100 – 80 = 20
$$
$$
\text{Step 2: Find the average of 80 and 100: } \frac{80 + 100}{2} = 90
$$
$$
\text{Step 3: Divide the difference by the average: } \frac{20}{90} = 0.2222
$$
$$
\text{Step 4: Multiply by 100: } 0.2222 \times 100 = 22.22
$$
$$
\text{Result: Percentage Difference is 22.22%.}
$$
Further Explained
Example: Compare 80 and 100.
Steps:
- Find the absolute difference between the values:
$$ 100 – 80 = 20 $$ - Find the average of the two values:
$$ \frac{80 + 100}{2} = 90 $$ - Divide the difference by the average:
$$ \frac{20}{90} = 0.2222 $$ - Convert to a percentage: Multiply by 100:
$$ 0.2222 \times 100 = 22.22\% $$ - Conclusion: The percentage difference is 22.22%.