How to get the percentage difference of two numbers

Percent difference formula is obtained by dividing the absolute value of change by the average of the values and then multiplying it with 100. To recall, a “per-cent” means a part per 100. The topic is of extreme importance and forms a major part of questions in most competitive exams. Among the different types of percentage questions, one of the most common question types involves the percentage difference formula. In this article, the percent difference formula is explained with solved example questions.

As stated, the percentage difference is be calculated by dividing the absolute value of the change by the average of the values and multiplying by 100.

∴ 

\(\begin{array}{l}\large Percent\: Difference\, Formula\,\left ( \%D \right ) = \frac{|n_{1}-n_{2}|}{\frac{n_{1}+n_{2}}{2}}\times 100\end{array} \)

Here, n1and n2 are the two different values.

With this formula, it is possible to determine the difference in percentage between any two values. It should be noted that as the absolute value is taken for the change (or difference) in values, the order of the numbers does not matter.

Important Note:

This formula should not be confused with the percentage increase or decrease which is- [(Difference) ÷ Original Number] × 100. To calculate percentage error, the difference between the approximate and exact value should be divided by the exact value and then multiplied by 100.

Example Questions Using the Percentage Difference Formula

Some problems related to the percent difference formula are given below for a better understanding of this concept.

Example 1:

A shopkeeper sells mangoes for Rs. 40 per kilos. Another shopkeeper sells the same mangoes for Rs. 60 per kilos. Find out how much is the percentage difference between the selling price of the shopkeepers.

Solution:

According to the formula, first, the difference between their selling price has to be calculated which is = Rs. 20

Now, 20 needs to be divided by the average of the selling prices and multiply by 100.

Average = (40 + 60)/2 = 50.

So, %D = (20 / 50) × 100 = 40%.

Example 2:

Find the percentage difference between the population of two cities having 12 million and 13 million population respectively.

Solution:

Putting the values of 1.2 million and 1.3 million in the above formula, the percent difference can be calculated.

Here, difference = |12,00,000 – 13,00,000| = 1,00,000.

Average = (12,00,000 + 13,00,000) = 12,50,000

%D = (1,00,000/ 12, 50, 000) × 100

So, percent difference = 8%.

Example 3:

In a cricket match, one team scored 220 runs while the other team managed to score 150 runs. What is the percentage difference between their runs?

Solution:

\(\begin{array}{l}\%D = \frac{|220-150|}{\frac{220+150}{2}}\times 100\end{array} \)

=(70/185) × 100

= 37.838%

Keep visiting BYJU’S to get more such maths formulas and lessons explained in a simple and easy to understand way.

The percentage difference is:

The difference between two values divided by the average of the two values. Shown as a percentage.

Difference means to subtract one value from another:

Example: Alex sold 15 tickets, and Sam sold 25

The difference between 25 and 15 is: 25 − 15 = 10

Average is the value halfway between:

average = first value + second value2

Example continued

The average of 25 and 15 is: (25 + 15) / 2 = 40/2 = 20

And then the difference as a Percentage of the average:

Example continued

• Difference is 25 − 15 = 10
• Average is (25 + 15) / 2 = 20
  

10 as a percentage of 20 is:

1020 × 100% = 50%

The percentage difference between 25 and 15 is 50%

Here is the answer, in one line:

Example continued

25 − 15(25 + 15)/2 × 100% = 50%

Now let's find out when, why and how to use it ...

When Should it be Used?

Percentage Difference is used when both values mean the same kind of thing (for example the heights of two people).

• But if there is an old value and a new value, we should use Percentage Change
• Or if there is an approximate value and an exact value, we should use Percentage Error

Why do we Average the Two Values?

Because there is no obvious way of choosing which value is the "reference" value.

Example continued

• If we use "15" we get 10/15 = 66.6...%
• If we use "25" we get 10/25 = 40%

But which one should we use? And if someone else did the calculations which one would they use?

So it is best to choose a value halfway between so there is no confusion.

What if the Difference is Negative?

We can't say which value is more important, so we can't say if the difference is "up" (positive) or "down" (negative) ... so we simply ignore any minus sign.

Example: Alex works 6 hours, and Sam works 9 hours

Difference = 6 − 9 = −3

But in this case we ignore the minus sign, so we say the difference is simply 3

(We could have done the calculation as 9 − 6 = 3 anyway,
as Sam and Alex are equally important!)

The Average is (6+9)/2 = 7.5

Percentage Difference = (3/7.5) x 100% = 40%

How to Calculate

Examples

Example: Juice costs $4 in one shop and $6 in another shop, what is the percentage difference?

• Step 1: The difference is 4 − 6 = −2, ignore the minus sign: difference = 2
• Step 2: The average is (4 + 6)/2 = 10/2 = 5
• Step 3: Divide: 2 by 5: 2/5 = 0.4
• Step 4: Convert 0.4 to percentage: 0.4×100 = 40%.

 The percentage difference is 40%

Another Example: There were 160 smarties in one box, and 116 in another box, what is the percentage difference?

160 to 116 is a difference of 44.

Average is (160+116)/2 = 276/2 = 138

44/138 = 0.319 (rounded to 3 places) = 31.9%

The percentage difference is 31.9%

The Formula

You can also put the values into this formula:

|First Value − Second Value(First Value + Second Value)/2| × 100%

(The "|" symbols mean absolute value, so any negatives become positive)

Example: "Best Shoes" gets 200 customers, and "Cheap Shoes" gets 240 customers:

|240 −200(240 + 200)/2| × 100% = |40/220| × 100% = 18.18...%

An interesting thing about this formula is that it doesn't matter which is the 1st or 2nd Value:

Put the values the other way around:

|200 − 240(200 + 240)/2| × 100% = |−40/220| × 100% = 18.18...%

The answer is the same (because we take the absolute value).

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