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Absolute Change and Relative Change

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Hi. This tutorial covers absolute change and relative change. When measuring variables, we expect them to change over time. It is important to quantify this change. Change can be represented as either absolute change or relative change. So let's define both of those two terms. So let's start with absolute change.

Absolute change is sometimes called absolute error if you're looking at maybe a prediction versus what actually happened. But the absolute change is the difference between a new value and an old value. So again, with difference, we're talking about subtraction.

Now, absolute change can be negative. So don't confuse absolute change with the math idea of absolute value. Absolute change can be negative. So just kind of as a formula, absolute change equals new value minus old value. So that's the difference between the new and the old so new minus old. And it does need to be in that order. New always needs to be first, and then you're subtracting the old. So that's absolute change.

Relative change or relative error is now the absolute change divided by the old value. So this is now a ratio. So the relative change is usually expressed as a percent. So now, your relative change is going to be your new value minus your old value. Again, this is just your absolute change. That's what we have here. So it's your absolute change divided by the old value. So it's new minus all divided by old.

So let's take a look now at an example. So suppose a small business owner is comparing last week's sales to the sales during the same week last year. Last week's sales were $4,825. And the sales for the same week last year were $6,012. So let's calculate the absolute change and the relative change. So let's start with absolute.

So your absolute change, again, is just your difference between your new and your old. So we need to take the new value and subtract the old value so $4,825 minus $6,012. So what I'll do is had that typed into my calculator. So that minus that. And I end up with negative $1,187. So my absolute change is that.

So this is negative, which means that last year, I made-- this business owner made more money in that specific week than this year. So again, we need to make sure we have that negative on there that shows that we have a decrease.

So now, let's go to-- let's calculate our relative change. So our relative change now is our absolute change divided by the old value. So in this case, since I've already calculated my absolute change, I'm going to take that number and divide it by my old value, so my old value here, which is $6,012.

So now, if I put that into my calculator, I'm going to do negative-- oops-- negative $1,187. And I'm going to divide that by the old value, which is $6,012. And I end up with negative 0.197. And I'll round that that way.

Now, if I write that as a percent, I multiply that by 100. And I get negative 19.7%. So that means that there was a decrease in sales of 19.7%. So that's two ways of expressing how the sales values changed from last year to this year. So that's a tutorial on absolute and relative change. Thanks for watching.