Percentage difference is a measure of the absolute difference between two values. The formula for calculating percentage difference is:
Percentage difference = (|New value - Original value| / Average of the two values) * 100, where
New value - Original value| represents the absolute difference between the two values.
Average of the two values = (New value + Original value) / 2
Proportion of difference = |New value - Original value| / Average of the two values
Percentage difference = Proportion * 100.
Percentage difference is used to compare the difference between two values as a percentage of their average value. It is a useful measure when you want to determine the relative difference between two values, regardless of whether the difference is positive or negative.
Suppose two students have different amounts of candies. One student has 20 candies and the other has 25 candies.
Percentage difference formula:
(|New value - Original value| / Average of the two values) * 100
Percentage difference = (5 / 22.5) * 100 = 22.22%
This means that the difference between the number of candies that the two students have is 22.22% of their average number of candies (22.5).
So, if you want to express the difference between the two students' number of candies as a percentage of their average, you can say it is 22.22%.
The percentage difference formula is used in various business contexts, including:
These are just a few examples of how the percentage difference formula is used in business contexts. The formula provides a quick and easy way to compare two values and to express the difference between the values as a percentage.
Here are some examples example problems that involve calculating percentage difference:
1. Price comparison: A store is selling a shirt for $20, and another store is selling the same shirt for $25. What is the percentage difference between the two prices?
Answer:
Percentage difference formula: (|New value - Original value| / Average of the two values) * 100
Average of the two values = (New value + Original value) / 2 = (25 + 20) / 2 = 22.5
Percentage difference = (5 / 22.5) * 100 = 22.22%
So, the percentage difference between the two prices is 22.22%.
2.Sales analysis: A company's sales were $50,000 last month, and this month they were $60,000. What is the percentage difference between the two sales figures?
Answer:
Percentage difference formula: (|New value - Original value| / Average of the two values) * 100
Percentage difference = (10,000 / 55,000) * 100 = 18.18%
So, the percentage difference between the two sales figures is 18.18%.
3. Market research: Company A has a market share of 30%, and Company B has a market share of 35%. What is the percentage difference between the two market shares?
Answer:
Percentage difference formula: (|New value - Original value| / Average of the two values) * 100
Percentage difference = (5 / 32.5) * 100 = 15.38%
So, the percentage difference between the two market shares is 15.38%.
4. Financial analysis: Last year, a company's expenses were $200,000, and this year they were $250,000. What is the percentage difference between the two expenses?
Answer:
Percentage difference formula: (|New value - Original value| / Average of the two values) * 100
Percentage difference = (50,000 / 225,000) * 100 = 22.22%
So, the percentage difference between the two expenses is 22.22%.
What you will learn from this article -
Percentage difference is a measure of the relative difference between two values. It represents the absolute difference between two values as a percentage of the average of the two values.
The formula for calculating percentage difference is as follows:
Percentage difference = (|New value - Original value| / Average of the two values) * 100
Where:
It's important to use the absolute value of the difference when calculating the percentage difference, because the result will always be a positive value, regardless of whether the New value is greater or less than the Original value.
Price comparison: A store is selling a shirt for $20, and another store is selling the same shirt for $25. What is the percentage difference between the two prices?
Answer:
So, the percentage difference between the two prices is 22.22%.
Sales analysis: A company's sales were $50,000 last month, and this month they were $60,000. What is the percentage difference between the two sales figures?
Answer:
So, the percentage difference between the two sales figures is 18.18%.
Market research: Company A has a market share of 30%, and Company B has a market share of 35%. What is the percentage difference between the two market shares?
Answer:
So, the percentage difference between the two market shares is 15.38%.
When calculating the percentage difference, it's important to use the absolute value of the difference between the two values, as the result should always be a positive value, regardless of whether the new value is greater or less than the original value.
Not using the absolute value of the difference can lead to negative values in the result, which is incorrect when calculating the magnitude of the change between two values. For example, if the original value is $100 and the new value is $80, the difference is -$20. However, the magnitude of the change is $20, not -$20.
Example 1: Comparing the prices of a product from two different years
Let's say that in 2022, the price of a television was $1000, and in 2023, the price of the same television decreased to $900. To calculate the percentage difference between the two prices, we use the following formula:
Percentage difference = |$900 - $1000| / ($900 + $1000) * 100 = $100 / $1900 * 100 = 5.26%
In this example, we use the absolute value of the difference, which is $100, to correctly capture the magnitude of the change.
Example 2: Comparing the number of people visiting a website
Let's say that in January 2022, a website had 10,000 visitors, and in February 2022, the number of visitors decreased to 9,000. To calculate the percentage difference between the two values, we use the following formula:
Percentage difference = |9,000 - 10,000| / (9,000 + 10,000) * 100 = 1,000 / 19,000 * 100 = 5.26%
In this example, we use the absolute value of the difference, which is 1,000, to correctly capture the magnitude of the change.
Example 3: Comparing the heights of two people
Let's say that person A is 6 feet tall and person B is 5 feet tall. To calculate the percentage difference between the two heights, we use the following formula:
Percentage difference = |6 - 5| / (6 + 5) * 100 = 1 / 11 * 100 = 9.09%
In this example, we use the absolute value of the difference, which is 1, to correctly capture the magnitude of the change.
When calculating the percentage difference, it's important to use the average of the two values as the denominator, as this provides a baseline for comparison.
Not using the average of the two values can lead to inaccurate results, as the magnitude of the change may be overstated or understated.
For example, if the original value is $100 and the new value is $200, the difference is $100.
However, if the denominator is only $100, the result will be 100%, which may not accurately reflect the magnitude of the change.
Example 1: Comparing the prices of a product from two different years
Let's say that in 2022, the price of a television was $1000, and in 2023, the price of the same television increased to $1100. To calculate the percentage difference between the two prices, we use the following formula:
Percentage difference = |$1100 - $1000| / ($1100 + $1000) / 2 * 100 = $100 / $2100 / 2 * 100 = 4.76%
In this example, we use the average of the two prices, which is $1100 + $1000 / 2 = $1050, as the denominator, to accurately reflect the magnitude of the change.
Example 2: Comparing the number of people visiting a website
Let's say that in January 2022, a website had 10,000 visitors, and in February 2022, the number of visitors increased to 12,000. To calculate the percentage difference between the two values, we use the following formula:
Percentage difference = |12,000 - 10,000| / (12,000 + 10,000) / 2 * 100 = 2,000 / 22,000 / 2 * 100 = 9.09%
In this example, we use the average of the two values, which is 12,000 + 10,000 / 2 = 11,000, as the denominator, to accurately reflect the magnitude of the change.
Example 3: Comparing the heights of two people
Let's say that person A is 6 feet tall and person B is 7 feet tall. To calculate the percentage difference between the two heights, we use the following formula:
Percentage difference = |7 - 6| / (7 + 6) / 2 * 100 = 1 / 13 /
Percentage difference = 1 / 13 / 2 * 100 = 7.69%
In this example, we use the average of the two heights, which is 7 + 6 / 2 = 6.5, as the denominator, to accurately reflect the magnitude of the change.
One common mistake in calculating percentage difference is neglecting the absolute value of the difference between the two values. The absolute value is used in the formula to eliminate negative results and represent the magnitude of the change regardless of the direction (increase or decrease). Neglecting the absolute value can lead to incorrect results, especially when comparing values that are decreasing.
Example 1: Comparing the prices of two items
Let's say that the price of a laptop was $1000 in January 2022 and decreased to $900 in February 2022. To calculate the percentage difference between the two values, we use the following formula:
Percentage difference = |$900 - $1000| / ($900 + $1000) / 2 * 100 = 100 / 1900 / 2 * 100 = 5.26%
Example 2: Comparing the number of people visiting a website
Let's say that in January 2022, a website had 10,000 visitors, and in February 2022, the number of visitors decreased to 8,000. To calculate the percentage difference between the two values, we use the following formula:
Percentage difference = |8,000 - 10,000| / (8,000 + 10,000) / 2 * 100 = 2,000 / 18,000 / 2 * 100 = 11.11%
Example 3: Comparing the heights of two people
Let's say that person A is 6 feet tall and person B is 5 feet tall. To calculate the percentage difference between the two heights, we use the following formula:
Percentage difference = |5 - 6| / (5 + 6) / 2 * 100 = 1 / 11 / 2 * 100 = 9.09%
Another common mistake in calculating percentage difference is using the wrong denominator. The formula for percentage difference requires using the average of the two values as the denominator. Using the wrong denominator can lead to incorrect results, especially when comparing values that are significantly different.
Example 1: Comparing the prices of two items
Let's say that the price of a laptop was $1000 in January 2022 and increased to $1200 in February 2022. To calculate the percentage difference between the two values, we use the following formula:
Percentage difference = |$1200 - $1000| / ($1200 + $1000) / 2 * 100 = 200 / 2200 / 2 * 100 = 9.09%
Example 2: Comparing the number of people visiting a website
Let's say that in January 2022, a website had 10,000 visitors, and in February 2022, the number of visitors increased to 12,000. To calculate the percentage difference between the two values, we use the following formula:
Percentage difference = |12,000 - 10,000| / (12,000 + 10,000) / 2 * 100 = 2,000 / 22,000 / 2 * 100 = 9.09%
Example 3: Comparing the heights of two people
Let's say that person A is 6 feet tall and person B is 7 feet tall. To calculate the percentage difference between the two heights, we use the following formula:
Percentage difference = |7 - 6| / (7 + 6) / 2 * 100 = 1 / 13 / 2 * 100 = 7.69%
One common error is mixing up the values when calculating the difference, which can result in a negative difference instead of a positive one. For example, if you are comparing the height of two people and you subtract the height of person A from person B, instead of person B from person A, the result will be negative. To avoid this, make sure to clearly label your values and double check your calculations.
Another common error is not taking the average of the two values when calculating the percentage difference. This can lead to an overestimation or underestimation of the difference, especially if the values are significantly different from each other. For example, if you are comparing the price of a product before and after a discount, taking the average of the two values before calculating the percentage difference will give you a more accurate result.
When calculating percentage difference, it's important to consider the units of measurement and make sure they are consistent. For example, if you are comparing the weight of two objects, you need to make sure they are measured in the same units (e.g. kilograms, pounds, etc.). If the units are different, the calculation of percentage difference will be incorrect.
A shirt was originally priced at $50. After a discount, the price was lowered to $40. What is the percentage difference between the original price and the discounted price?
Solution:
The difference between the original price and the discounted price is $50 - $40 = $10.
The percentage difference is calculated as:
Percentage difference = (difference / original value) * 100 = ($10 / $50) * 100 = 20%
So, the percentage difference between the original price and the discounted price is 20%.
A patient had a blood pressure reading of 120/80 mmHg last year and 130/85 mmHg this year.
What is the percentage difference between the two readings?
Solution:
An investment in a stock was worth $1000 a year ago and is now worth $1100. What is the percentage difference between the current value and the original value?
Solution
The difference between the current value and the original value is $1100 - $1000 = $100.
The percentage difference is calculated as:
Percentage difference = (difference / original value) * 100 = ($100 / $1000) * 100 = 10%
So, the percentage difference between the current value and the original value is 10%.
I hope these examples help to clarify the concept of percentage difference and how it is used in different industries.
Problem 1:
A shirt was priced at $50 and after a discount, the price was lowered to $40. What is the percentage difference between the original price and the discounted price?
Solution: The difference between the original price and the discounted price is $50 - $40 = $10. The percentage difference is calculated as: Percentage difference = (difference / original value) * 100 = ($10 / $50) * 100 = 20%. So, the percentage difference between the original price and the discounted price is 20%.
Problem 2:
A bottle of shampoo was priced at $6 and after a price increase, it was priced at $7. What is the percentage difference between the original price and the increased price?
Solution: The difference between the original price and the increased price is $7 - $6 = $1. The percentage difference is calculated as: Percentage difference = (difference / original value) * 100 = ($1 / $6) * 100 = 16.67%. So, the percentage difference between the original price and the increased price is 16.67%.
Problem 3:
A student scored 80 marks out of 100 in an exam last year and 90 marks out of 100 in the same exam this year. What is the percentage difference between the marks scored this year and last year?
Solution: The difference between the marks scored this year and last year is 90 - 80 = 10. The percentage difference is calculated as: Percentage difference = (difference / original value) * 100 = (10 / 80) * 100 = 12.5%. So, the percentage difference between the marks scored this year and last year is 12.5%.
Problem 4:
A product was priced at $100 and after a discount, it was priced at $90. What is the percentage difference between the original price and the discounted price?
Solution: The difference between the original price and the discounted price is $100 - $90 = $10. The percentage difference is calculated as: Percentage difference = (difference / original value) * 100 = ($10 / $100) * 100 = 10%. So, the percentage difference between the original price and the discounted price is 10%.
Problem 5:
A company's sales increased from $10,000 to $12,000. What is the percentage difference between the sales this year and last year?
Solution: The difference between the sales this year and last year is $12,000 - $10,000 = $2,000.
The percentage difference is calculated as: Percentage difference = (difference / original value) * 100 = ($2,000 / $10,000) * 100 = 20%. So, the percentage difference between the sales this year and last year is 20%.
Problem 6:
A product was priced at $200 and after a price increase, it was priced at $250. What is the percentage difference between the original price and the increased price?
Solution: The difference between the original price and the increased price is $250 - $200 = $50. The percentage difference is calculated as: Percentage difference = (difference / original value) * 100 = ($50 / $200) * 100 = 25%.
So, the percentage difference between the original price and the increased price is 25%.