## What Is the Percent Difference in Math?

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

Percent Difference $= \frac{Absolute \; Difference}{Average} \times 100$

In simple words, the percent difference is the percentage of the relative difference. The relative difference between two quantities compares the difference between the two values in relation to their average.

Relative Difference $= \frac{Absolute \; Difference}{Average}$

The percent difference is frequently used when comparing data sets or estimating the degree of change between two numbers.

Note that the “percent difference” and the “percent change” are two different concepts. We will compare them later in the article. Also, do not confuse this formula with the percent decrease or increase formulas.

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## What Is the Percent Difference Formula?

The percentage difference is the ratio of the difference in their values to their average, multiplied by 100.

Percent difference formula for the two values A and B can be given as

Percent difference $= \frac{A – B}{ \frac{(A + B)}{2}} \times 100$

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## How to Find Percent Difference

Follow the steps given below to learn how to calculate the percent difference between two values A and B.

**Step 1:** Find the absolute difference.

Find the absolute value of the difference between A and B. The order does not matter since we will be taking the absolute value.

Absolute Difference $= |A \;-\; B|$

**Step 2:** Find the average of A and B. Simply add the values together and divide the sum by 2.

Average $= \frac{(A + B)}{2}$

**Step 3:** Divide the absolute difference by the average and multiply by 100 in order to calculate the percent difference.

Percent Difference $= \frac{Absolute \; Difference}{Average} \times 100$

Percent difference $= \frac{|A \;-\; B|}{ \frac{(A + B)}{2}} \times 100$

## Percent Difference between Two Numbers

The percent difference between the two numbers is expressed as follows:

Percent Difference $= \frac{|A – B|}{ \frac{(A + B)}{2}} \times 100$

**Example: Alex has 10 years of working experience. Paxton has 20 years of working experience. What is the percent difference?**

Here, $A = 10, B = 20$

Note that these values represent the working experience of Alex and Paxton in years.

Can you decide which value is more important here? No, both values hold the same importance!

In such cases, we can use the percent difference formula.

We choose the average value as the reference point. We take absolute difference to treat both values equally. So, the order does not matter when you subtract.

$|A \;-\; B| = |10 \;-\; 20| = | \;-\;10| = 10$

$\frac{(A + B)}{2} = \frac{10 + 20}{2} = 15$

Percent Difference $= \frac{|A – B|}{\frac{(A + B)}{2}} \times 100$

Percent Difference $= \frac{10}{15} \times 100$

Percent Difference $≈ 66.67\%$

## Percent Difference vs. Percent Change

Percent Difference | Percent Change |
---|---|

Percent Difference $= \frac{|A – B|}{\frac{(A + B)}{2}}100$ | Percent Change $= \frac{(Final \;Value\; -\; Initial \;Value)}{Initial \;Value} \times 100$ |

It is calculated by taking the absolute difference between the two values, dividing it by the average of the two values, and multiplying by 100. | It is calculated by taking the absolute change, dividing it by the initial value, and multiplying by 100. |

Reference point is the average of two values. | Reference point is the initial value. |

We ignore the minus sign as we take the absolute value of the difference. | If the value is positive, it means there is an increase. If the value comes out to be negative, it indicates a decrease. |

## Facts about Percent Difference

- The context of the data being analyzed should be regarded when interpreting percent differences.
- The percent difference just measures the relative difference between two values and does not reveal the pattern or direction of change. It does not distinguish between positive and negative changes.
- When there is an old value and a new value, we should use the percentage change formula.
- When there is an approximate value and an exact value, we should use the percentage error formula.
- When both the values have equal importance or when it is not possible to determine the reference value, we use the percent difference formula.

## Conclusion

You know the percent difference, definition, concept, formula, etc. Let’s move toward the numerical section of a percent difference, including solved examples and MCQs, for a clearer understanding.

## Solved Examples on Percent Difference

**1. Mr. Dunphy’s garden has 78 rose plants. Mr. Prichet’s garden has 106 rose plants. Find the percent difference.**

**Solution:**

Firstly, we will calculate the difference between the two numbers.

Difference $= 78\;-\;106 = \;-\; 28$

We can remove the negative sign by giving the absolute value of the difference.

Absolute Difference $= |Difference| = |\;-\;28| = 28$

Average $= \frac{78 + 106}{2} = \frac{184}{2} = 92$

Now, find the percentage difference.

Percentage Difference $= (\frac{Absolute \;Difference}{Average}) \times 100$

Percentage Difference $= \frac{28}{92} \times 100$

Percentage Difference $≈ 30.43\%$

**2. In a video game tournament, Team A scored 980 and Team B scored 1220 points. What is the percentage difference between the scores?**

**Solution:**

On calculating the difference between the two scores, we get

Difference $=$ Score of Team B – Score of Team A $= 1220\;-\;980 = 240$

Absolute difference $= | 240 | = 240$

Average $= \frac{1220 + 980}{2} = 1100$

Now, we can calculate the percentage difference between the teams’ scores.

Percentage Difference $= (\frac{Difference}{Average})\times100$

Percentage Difference $= (\frac{240}{1100}) \times 100$

Percentage Difference $≈ 21.81\%$

**3. What is the percentage difference between 7.2 and 8.5?**

**Solution:**

Here, we have to calculate the difference between two numbers.

Difference $= 7.2 \;-\; 8.5 = \;-\; 1.3$

We will remove the negative sign by taking the absolute value of the difference.

Absolute Difference $= |Difference| = |\;-\;1.3| = 1.3$

Now, you can calculate the percentage difference.

Average $= \frac{7.2 + 8.5}{2} = 7.85$

Percentage Difference $= (\frac{Absolute \;Difference}{Average}) \times 100$

Percentage Difference $= (\frac{1.3}{7.85}) \times 100$

Percentage Difference $≈ 16.56\%$

## Practice Problems on Percent Difference

## How to Calculate Percent Difference - Definition, Formula, Examples

### The population of two cities A and B is 50,000 and 55,000 respectively. What is the percentage difference?

Population difference $= 55,000 \;-\; 50,000 = 5,000$

Average $= \frac{(50,000 + 55,000)}{2} = 52,500$

Percent difference $= \frac{5,000}{52,500} \times 100 ≈ 9.52\%$

### The weight of an object A is 200 grams. The weight of object B is 180 grams. What is the percent difference?

Percent Difference $= \frac{|Weight \;difference|}{(Average\; weight)} \times 100$

Percent Difference $= (\frac{20}{190}) \times 100$

Percent Difference $≈ 10.53\%$

### The population of town A is 10,000 and that of B is 12,500. What is the percent difference?

Difference $= 12,500 \;-\; 10,000 = 2,500$

Average$ = 11,250$

Percent difference $=(\frac{2,500}{11.250}) \times 100 ≈ 22.22\%$

### The price of a watch is $\$80$. The price of a clock is $\$58$. Choose the correct percent difference in the price.

Difference $= \$80 \;-\; \$58 = \$22$

Average $= 69$

Percent difference $=(\frac{16}{72}) \times 100 ≈ 32\%$.

## Frequently Asked Questions on Percent Difference

**Why do we take the average of two values in the percent difference formula?**

Since there is no way to decide which value is the reference value, we consider the average of two values as the reference value. It helps us treat both the values equally.

**Why do we ignore the minus sign when calculating the percent difference?**

Since we focus on the magnitude of the change (regardless if it is positive or negative) and not on the direction of the change, we don’t take the minus sign into account. Since both the values are equally important, the use of the negative sign is not useful.

**When do we use the percent error formula?**

When we want to compare the exact value with the estimated value (or measurement), we prefer the percent error formula. It helps us quantify the accuracy or precision of a measurement.

**What does percent change, percent error, and percent difference tell us?**

Percent change generally indicates growth or decline, the percent error measures accuracy in the measurement, and the percent difference helps us quantify variation or inconsistency in the two values.