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4 Tutorials that teach Using Percentages in Statistics

# Using Percentages in Statistics

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Author: Sophia Tutorial
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This lesson will investigate some of the uses of percentages in statistics.

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Tutorial
This tutorial will discuss how to use percentages wisely in statistics by focusing on:
1. Percentage Point vs. Percent

## 1. Percentage Point vs. Percent

People tend to use percentages without really thinking about what type of percentages they're talking about. Results and statistics are often expressed as percents but it's important to distinguish between percentage points and percents, which are used to describe relative change. Percentage points are used to measure absolute change.

Percentage points measure absolute change and percents are used to describe relative change.}}

The best way to explain the difference is to show you. Suppose a teacher gives a particularly difficult exam and these six students all failed it.

The teacher graciously offered a retake to the students. How did they do?
They all passed, so that's great. Jonathan scored an 88, Ryan scored a 78, Katherine scored an 84, etc. And look at Kelly, 95%. Nicely done, Kelly.

These changes can be expressed as percentage points and percent increase. Which student had the highest increase in percentage points? Jonathan went from 52% to 88%, that's an increase of 36 percentage points. Ryan went from 38% to 78%, that's an increase of 40 percentage points.

We can calculate that for all of them and see that it was Kelly who increased 47 percentage points.

Now, who had the highest percent increase? Now you need to look at the raw increased numbers. 36 percentage points for Jonathan, 40 percentage points for Ryan, 23 percentage points for Katherine, etc. And determine who had the highest percent increase over their old score. And so you begin with the 52 and determine how much of an increase 36% was over that 52.

Jonathan's score increased by 69%. Katherine's only increased by 38%, because she had a fairly high score to begin with. Which student had the highest percent increase?

It was Ryan. He more than doubled his score. He started with a 38 and finished with a 78, a 40 percentage point increase. 40 percentage point increase over a score of 38, is over 100%. He more than doubled his old score.

Percentage Points
An absolute increase or decrease in a percent value.
Percent Change
A relative increase or decrease in a percent value.
Percentage points measure absolute change and percents are used to describe relative change.
A politician's approval rating drops from 34.3% down to 26.9%.

Question: What was the absolute change in his approval rating?

Recall the difference between percents and percentage points. What is the difference?

Answer: 26.9 minus 34.3. This is negative 7.4 percentage points. He dropped 7.4 percentage points.

Question: What was his relative change, his percent change?
Answer: Start with the negative 7.4 percentage point drop. How does that compare to his old percent of 34.3? It was negative 21.6%. It was a 21.6% decrease in his approval rating. That's a huge dip.

He must have done something really, really wrong to drop from 34.3%, which wasn't high to begin with, all the way down to something like 27%.

When percentages are used in statistics it's important to know whether the focus is absolute change or relative change. Absolute change is the difference in percentage points and relative change is a percent increase or percent decrease.

Source: this work is adapted from sophia author jonathan osters.

Terms to Know
Percent Change

A relative increase or decrease in a percent value

Percentage Points

An absolute increase or decrease in a percent value.