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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.
Percent change describes the relative change (increase or decrease) in a percent value. Percentage points are used to measure absolute change.
Suppose a teacher gives a particularly difficult exam, and these six students all failed it. The teacher graciously offered a retake to the students, and they all passed.
The table below shows their original score and their retake score. On the retake, Jonathan scored an 88, Ryan scored a 78, Katherine scored an 84, etc.
| Student | Original Score | Retake Score |
|---|---|---|
| Johnathan | 52% | 88% |
| Ryan | 38% | 78% |
| Katherine | 61% | 84% |
| Isaiah | 44% | 89% |
| Teri | 50% | 82% |
| Kelly | 48% | 95% |
These changes can be expressed as either percentage points or percent increase. First, which student had the highest increase in percentage points?
| Student | Original Score | Retake Score | Change in Percentage Points |
|---|---|---|---|
| Johnathan | 52% | 88% | 36% |
| Ryan | 38% | 78% | 40% |
| Katherine | 61% | 84% | 23% |
| Isaiah | 44% | 89% | 45% |
| Teri | 50% | 82% | 32% |
| Kelly | 48% | 95% | 47% |
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 and determine who had the highest percent increase over their old score.
Begin with Jonathan's scores. We need to determine how much of an increase 36 percentage points is over that original score of 52.
| Student | Original Score | Retake Score | Change in Percentage Points | Percent Increase |
|---|---|---|---|---|
| Johnathan | 52% | 88% | 36% | 69% |
| Ryan | 38% | 78% | 40% | 105% |
| Katherine | 61% | 84% | 23% | 38% |
| Isaiah | 44% | 89% | 45% | 102% |
| Teri | 50% | 82% | 32% | 64% |
| Kelly | 48% | 95% | 47% | 98% |
Jonathan's score increased by 69%. Katherine's score only increased by 38% because she had a fairly high score to begin with.
But it was Ryan who had the highest percent increase. He started with a 38 and finished with a 78, a 40-percentage-point increase. A 40-percentage-point increase over a score of 38 is over 100%, meaning he more than doubled his old score.
Suppose Patrick has found his way to class president at Memorial High School. But his approval rating has just hit the skids, dropping from 56% to 42%.
First, let’s determine the absolute change in his approval rating. Take 42 and subtract 56 from it.
However, how does that drop look when you calculate it in terms of relative change? Take the 14-percentage-point drop and divide it by the original approval rating, 56.
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