# Calculating Percentage Point

By Kathleen Knowles, 03 Jul 2020

In mathematics, there are various metrics used to simplify or explain events or outcomes - especially those that involve changes or comparison. Some of these metrics include ratios, percentages, and percentage points.

Ratios express the quantitative relationship between values by showing how many times one is contained in another. Percentages are similar to ratios, but they're expressed as a fraction of 100.

Percentage point, on the other hand, is a unit of measurement that represents the difference between two percentages.Percentage point is often represented as "pp" or "p.p." In other books, it is written in full as “percentage points” or “percent points” to avoid confusing it with “pages.”

## Understanding Percentage Point

Percentage point is used in a wide range of applications, ranging from probability studies to fault/ risk analysis to descriptive statistics to investment predictions. Many statisticians and analysts prefer the use of percentage points to percentages when comparing amounts. Some examples to illustrate the percentage point calculations are given below:

### Example 1

In 2018, at St. Andrew’s Catholic Boys’ School, forty percent (40%) of students passed the A levels mock examinations that were administered by the state. In 2019, in the same school, sixty-five percent (65%) of students passed the same examinations, and in 2020, 69% were successful. What is the change in the examination success rates between 2018 and 2019?

To calculate the percentage point, follow these steps:

Step 1: Highlight the percentages you need to compare. In this case, we have 40% (2018) and 65% (2019)

Step 2: Subtract the smaller percentage from the larger percentage

Change in exam success rates = 65 - 40 = 25

Step 3: Add your unit (percentage points): The difference in exam success rates between 2018 and 2019 is 25 percentage points.

In the example above, we can say that there was an increase in the success rate by 25 pp.

## Distinguishing Between Percentage and Percentage Point

In texts and even in presentations, percentage and percentage points are often interchanged. However, using one in place of the other can give the information being conveyed a completely different meaning.

To illustrate this, imagine if the government increases taxes from 4% to 6%, that’s a 50 percent tax increase but a 2-percentage point tax increase. Example 2 shows how similar calculations can be done.

### Example 2

In a survey of road accidents in Durban, South Africa, it was discovered that during the rainy season of 2006, eighty percent (80%) of car accidents involved men. The same survey showed that in the dry season in 2007, that figure dropped to sixty percent (60%). Compare the changes in percentage and percentage points.

Step 1: Highlight the percentages you need to compare. In this case, we have 80% (rainy season) and 60% (dry season).

Step 2 (For the percentage): Subtract the smaller percentage by the larger percentage and divide the quotient by the larger percentage:

Percentage change = ((80 - 60)/80) * 100

This gives us: (20/80) * 100 = 25

Step 3: Add your unit (%). There was a 25% decrease in the number of accidents involving men during the dry season.

Step 4: (For the percentage point): Subtract the smaller percentage from the larger percentage

Change in number of accidents involving men = 80 – 60 = 20

Step 5: Add your unit (percentage points): The difference between the accidents involving men in the rainy season and the dry season is 20 pp.

From the results above, we can see that the percentage difference is 25%, while the percentage point is 20 pp.

## Deriving Percentage Point from Ratios

To derive percentage points from ratios, the rations have to be converted to percentages, which can be subtracted to obtain the percentage points. This is further explained in the example below.

### Example 3

In January 2020, the P.E teacher, Mr. Percy, started a Yoga class for teenagers aged between 12 and 17. The ratio of boys to girls in the class was 3:7. The total number of children that signed up was 20. Unfortunately, schools had to be closed down due to a pandemic.

After the pandemic, only half of the students that signed up initially returned. Of this lot, the ratio of boys to the total number was 2:5. Find the changes in the number of boys and girls using percentage points.

Step 1: Convert the ratios to percentages

#### Before the Pandemic

Combining the ratio, we have 3 + 7 = 10

Therefore, there are (3/10) * 100% boys and (7/10) * 100% girls.

This gives us 30% boys and 70% girls.

#### After the Pandemic

If the ratio of boys to the total number is 2:5, then the percentage of boys is given as (2/5) * 100% = 40%

Therefore, there are 40% guys left and 60% girls left

Step 2: Highlight the percentages you need to compare. In this case, we have the following:

• For boys: 30% (Before the pandemic) and 40% (After the pandemic)
• For girls: 70% (Before the pandemic) and 60% (After the pandemic)

Step 3: Subtract the smaller percentage from the larger percentage

• For boys: Change in the percentage of boys = 40 – 30 = 10 (increase)
• For girls: Change in the percentage of girls = 70 -60 = 10 (decrease)

Step 4: Add your unit (percentage points): The difference in the percentage of boys at the Yoga class before and after the pandemic is 10 pp (increase).

The difference in the percentage of girls at the Yoga class before and after the pandemic is 10 pp (decrease).

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