Percent Difference Formula: Examples, Facts, Practice Problems

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What Is the Percent Difference Formula?

The percentage difference formula calculates the percent difference by taking the absolute difference between the two values, dividing it by the average of the two values and multiplying the result by 100.

Percent difference formula is simply the ratio of the absolute difference to the average of two values, calculated as a percentage.

Percentage difference $= \frac{Absolute \;difference}{Average} \times 100$

The percentage difference formula is particularly useful when the direction of change is not known. It allows us to understand the magnitude of change between two values, when there is no way of choosing the reference value.

Percent Difference Formula

Percentage difference $= \frac{Absolute\; difference}{Average} \times 100$

The percent difference formula (% difference formula) for two values, a and b can be given as

Percentage difference $= \frac{\frac{|a – b|}{a + b}}{2} \times 100$

In the context of percent difference, it is common practice to ignore the minus sign and consider the absolute value of the difference. This is because the goal is to determine the magnitude of the change (variation), regardless of whether it is an increase or a decrease.

By taking the absolute value of the difference, we can focus on the magnitude of the change rather than the direction. This allows for a standardized approach in comparing values and expressing the difference as a positive percentage.

How to Calculate Percent Difference in Math

Let’s take an example to understand the steps to calculate percent difference.

Example: The price of item A is $\$30$. The price of item B is$\$50$. Calculate the percent difference between two prices.

Step 1: Identify the two values.

In this example, the values we are comparing are 30 and 50.

$a = 30, b = 50$

Step 2: Find the absolute difference.

Difference $= a – b$

Difference $= 30 – 50 = -20$

Absolute Difference $= |Difference|$

Absolute Difference $= |- 20|= 20$

(Note: The order of numbers doesn’t matter as we calculate the absolute difference between the two numbers.)

Step 3: Calculate the average of both the values.

Average $= \frac{a + b}{2} = \frac{a + b}{2} \frac{30 + 50}{2} = \frac{80}{2} = 40$

Step 4: Use the percent difference formula to calculate the percent difference.

Percentage difference $= \frac{\frac{|a – b|}{a + b}}{2} \times 100$

Percentage difference $= \frac{20}{40}\times 100$

Percentage difference $= 0.5 \times 100$

Percentage difference $= 50\%$

Thus, the percent difference between 30 and 50 is $50\%$.

When to Use the Percent Difference Formula

• Note that the context is important when deciding the suitable formula. When both the values belong to the same category or have the same importance, use the percent difference formula.

For example, comparing weights or heights of two kids.
• If the magnitude of change is more important than the direction of the change, then the percent difference formula is more suitable.

For example, Anna works 9 hours a day, whereas her husband works 8 hours a day. Here, when we compare these two numbers, the magnitude of change is more important. Positive or negative does not matter here.
• Understand the reference value against which you want to compare the difference between the values. If both the values have equal importance, and there is no way of choosing a reference point, choose the percent difference formula.

For example, Roy has $\$26$, and Joy has$\$15$. How do we choose a reference value here? So, we go for the average value and use the percent difference formula.

• Percent difference is a measure of the relative change or variation between two values, expressed as a percentage.
• Percent difference is always positive, as it represents the magnitude of change or deviation between the values, regardless of the direction of change.
• A higher percent difference indicates a larger relative change between the values, while a lower percent difference suggests a smaller relative change.
• Percent difference should be used with caution when dealing with values close to zero or values that can be negative, as it may lead to inaccurate interpretations. In such cases, alternative measures such as percentage change between two numbers or relative difference may be more appropriate.

Conclusion

In this article, we learned about the percent difference formula and how to calculate percent difference. Understanding percent difference allows meaningful comparisons and analysis of changes between two values, providing valuable insights into trends and variations. Let’s solve some examples and practice problems to understand the concept better.

Solved Examples on Percent Difference

1. The price of a sweater is $\$80$, and the price of a jacket is$\$96$. Calculate the percentage difference.

Solution:

$a = \$80$and$b = \$96$

Now, let’s calculate the absolute difference between the two values.

Difference $= |\$80 – \$96| = |-\$16| = \$16$

Now, we will calculate the average of the two values.

Average $= \frac{a + b}{2} = \frac{80 + 96}{2} \frac{176}{2} = 88$

Percentage difference $= \frac{\frac{|a – b|}{a + b}}{2} \times 100$

Percentage difference $= \frac{16}{88} \times 100$

Percentage difference $= 0.1818 \times 100$

Percentage difference $= 18.18\%$

2. The population of town X is 20,000. The population of town Y is 16,000. What is the percent difference between the population values?

Solution:

$a = 20,000$

$b = 16,000$

Absolute difference $= |20,000 – 16000| = |4000| = 4000$

Now we will calculate the average of the two values:

Average $= \frac{a + b}{2} = \frac{20,000 + 16,000}{2} \frac{36,000}{2} = 18,000$

Percentage difference $= \frac{\frac{|a – b|}{a + b}}{2} \times 100$

Percentage difference $= \frac{4000}{18000} \times 100$

Percentage difference $= 0.2222 \times 100$

Percentage difference $= 22.22\%$

3. What is the percent difference between 5000 and 7000?

Solution:

Let’s name the value 5000 as “a” and the value 7000 as “b”.

The absolute difference $= |5000 – 7000| = |- 2000| = 2000$

Now we will calculate the average of the two values:

Average$= \frac{a + b}{2} = \frac{5,000 + 7,000}{2} \frac{12,000}{2} = 6000$

Percentage difference $= \frac{\frac{|a – b|}{a + b}}{2} \times 100$

Percentage difference $= \frac{2000}{6000} \times 100$

Percentage difference $= 0.3333 \times 100$

Percentage difference $= 33.33\%$

4. The temperature of a city A is 20C. The temperature of a city B is 26C. Find percent difference between the temperature values.

Solution:

$a = 20$

$b = 25$

The absolute difference $= |20 – 26| = |- 6| = 6^{\circ}$

Now we will calculate the average of the two values:

Average $= \frac{a + b}{2} = \frac{20 + 26}{2} \frac{46}{2} = 23$

Percentage difference $= \frac{\frac{|a – b|}{a + b}}{2} \times 100$

Percentage difference $= \frac{6}{23} \times 100$

Percentage difference $= 0.2608 \times 100$

Percentage difference $= 26.08\%$

5. Alex finished a task in 2 hours. Tony completed the same task in 1.5 hours. What is the percent difference?

Solution:

$a = 2 hr$

$b = 1.5 hr$

The absolute difference $= |2 – 1.5| = |0.5| = 0.5$

Now we will calculate the average of the two values:

Average $= \frac{a + b}{2} = \frac{2 + 1.5}{2} \frac{3.5}{2} = 1.75$

Percentage difference $= \frac{\frac{|a – b|}{a + b}}{2} \times 100$

Percentage difference $= \frac{0.5}{1.75} \times 100$

Percentage difference $= 0.2857 \times 100$

Percentage difference $= 28.57\%$

Practice Problems on Percent Difference

1

What is the formula for calculating percent difference?

$\frac{\frac{|a - b|}{a + b}}{2} \times 100$
$\frac{\frac{|a + b|}{a + b}}{2} \times 100$
$\frac{\frac{|a - b|}{a - b}}{2} \times 100$
$\frac{|a - b|}{a + b} \times 100$
CorrectIncorrect
Correct answer is: $\frac{\frac{|a - b|}{a + b}}{2} \times 100$
The percent difference formula calculates the difference between two values and expresses it as a percentage of the average of those values.
2

Percent difference =

$\frac{Absolute \;difference}{Average} \times 100$
$\frac{Sum}{Average} \times 100$
$\frac{DifferenceInitial}{value} \times 100$
None of the value
CorrectIncorrect
Correct answer is: $\frac{Absolute \;difference}{Average} \times 100$
Percent difference $= \frac{Absolute\; difference}{Average} \times 100$
3

What does percent difference measure?

Growth or decline over time
Accuracy of a measurement
Variation or discrepancy between two values
Direction of change
CorrectIncorrect
Correct answer is: Variation or discrepancy between two values
Percent difference measures magnitude of change, variation or discrepancy between two values.