Absolute Change and Relative Change

Video Transcription

In this tutorial, we're going to talk about the difference between absolute change, which is just a raw number, and relative change, which relates it back to what used to be the value.

Let's give an example first off. Suppose an infant weighed 6 and 1/2 pounds at birth, and one year later, weighed 14 and 1/2 pounds. Which of the following are true statements? Is it true that the infant's weight change was an increase of eight pounds? Well, that's a true statement. 14.5 minus 6.5 is 8 pounds. It increased by 8 pounds.

How about B? The infant's weight change was an increase of 123%. Well, this one's a little bit less obvious, but it's also true. The eight-pound increase was more than double what the birth weight was. So it was an increase of over 100%. And in fact, when you do the calculation, 8 divided by 6.5 is 123%.

So absolute change is the actual change in units. In the last example, it was pounds. But it could be degrees, inches, percentage points, or lots of different things. By percentage points, I mean that suppose a political candidate's approval rating went up from 44% to 48%. That absolute change is four percentage points. Relative change is the percent difference from the previous value. And it's always expressed as a percent.

So let's go back. How do you calculate absolute change or absolute difference is another word for it? Well, you simply do the difference between the new and the old-- 14.5 minus 6.5. That's a difference of 8 pounds. And it's positive 8 pounds because it went up.

Compare that with the relative change or the relative difference. It's calculated by taking the absolute difference, which was 8 pounds, and dividing by what it used to be, 6.5. So it increased by 8 over the 6 and 1/2. When you put this into a calculator, you get 1.23. When expressed as a percent, 1.23 is 123%. That means that there was a 123% increase over the birth weight. That was the relative change.

Let's do an example. Which of the following states in the table had the highest absolute change from 1990 to 2000? These are the results of the 1990 census and the 2000 census. And I want to know which of the following states from Florida to Kansas alphabetically have the highest absolute change between that time? Hit the Pause button, and calculate it.

You should have come up with these numbers for the absolute change. All of the states in the list had increases in the population. Some were not very much, like Hawaii, which only had about a 100,000-person increase. Some were a lot, like Georgia and Florida, which increased by over a million people. The highest absolute change was 3,044,452 people in Florida.

Now, the question of which state had the largest relative change from 1990 to 2000 is a little bit different. What we need to do is figure out if 3 million was a large change percentage-wise from the old population of about 13 million. Was that a large increase? Well, sure, it was a large increase. But was it the largest percent increase in the list? Hit pause, and determine the percent increases for each of these states.

What you should have come up with is the following percentages. Florida's relative change was positive 24%-- 3 million, about, divided by about 13 million gives you about 24%. Georgia's increase was about 26%, a little bit larger of a percent increase than Florida. But it wasn't the highest of the list. The highest of the list was a 29% increase in the state of Idaho. Now, notice it didn't have a very large absolute change. But its population wasn't very big to begin with, and so even a small absolute change can be a large relative change.

And to recap, absolute change is the absolute difference in raw numbers. It's the change in units. Relative change examines how the new number compares to the previous number in terms of a percent. Did it go up by 10%? Did it go down by 7%? What happened percentage-wise from then to now? So the terms we used were absolute difference and absolute change, same thing, and relative difference and relative change.

Good luck, and we'll see you next time.