Absolute Change and Relative Change

1. Absolute Change and Relative Change

Absolute change is the actual change in units. It could be the actual change in pounds, degrees, inches, percentage points, or lots of different things. Relative change is the percent difference from the previous value, and it's always expressed as a percent. Let’s look at some real world statements of absolute and relative change.

EXAMPLE

An infant weighed 6.5 pounds at birth, and one year later, weighed 14.5 pounds. Consider the following statements:

• Statement 1: The infant's absolute weight change was an increase of eight pounds.
• Statement 2: The infant's relative weight change was an increase of 123%.

Let’s look at what makes these statements true.

terms to know

Absolute Change

The raw increase or decrease in the value of a variable.

Relative Change

The percent increase or decrease in the value of a variable.

2. Calculating Absolute Change

How do you calculate absolute change? Another word for it is the absolute difference. You simply calculate the difference between the new and the original.

formula to know

Absolute Change

EXAMPLE

Consider the example above where an infant weighed 6.5 pounds at birth, and one year later, weighed 14.5 pounds.

So, 14.5 minus 6.5 was a difference of 8 pounds.



It is also a positive 8 pounds because it went up from 6.5 to 14.5 So, the infant's absolute weight change was an increase of eight pounds (Statement 1).

3. Calculating Relative Change

The relative change, or the relative difference, is calculated by taking the absolute difference and dividing it by its originating value.

formula to know

Relative Change

EXAMPLE

In the example above, the new value was 14.5 pounds and the original value was 6.5 pounds, which gives us an absolute change of 8 pounds. You can plug these values into either relative change formula:





When you plug these values into the relative change formula, you get 1.23. Lastly, we convert the decimal to a percent. Again, we can convert to a percent by moving the decimal to the right two decimal places.

When expressed as a percent, 1.23 is 123%. So, the infant's relative weight change was an increase of 123% (Statement 2).

4. Real World Example of Absolute Change and Relative Change

Consider the following example that shows a list of state populations in 1990 and 2000. We can determine which state has the highest absolute change and which has the highest relative change.

The equation for absolute change is . To calculate the absolute change, simply subtract the 1990 value from the 2000 value. Let’s take Florida as an example.

We can calculate the absolute change for the rest of the states in the same way.

All of the states on 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 onto the relative change. The equation for relative change is:

To find the relative change, take each absolute change and divide it by the original population from 1990. Let’s use Florida as an example and try to find the relative change of the population.

We can complete the calculations for the rest of the states the same way.

Florida's relative change was positive 24%—approximately 3 million divided by 13 million gives you about 24%. Georgia's increase was about 26%, a little bit larger than Florida. The highest of the list was a 29% increase in the state of Idaho. 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.

big idea

Here's a breakdown of the distinction between the two categories. Absolute change is the difference in raw numbers. In this case, it's the actual change in enrollment from one year to the next. Whereas, the relative change converts how one year compared to the next in terms of a percent of the original number.

did you know

Looking at the absolute change and relative change can tell different stories, and oftentimes these stories are a valuable way to analyze data.

5. Positive and Negative Change

Absolute change and relative change can be positive or negative. If the new value is larger than the original value, there was an increase, and the changes will be positive. If the new value is less than the original value, then there is a decrease and the changes will be negative. Let’s look at some examples.

EXAMPLE

In 2014, there were 120 students enrolled in a local dance school. In 2015, there were 108 students enrolled in the same school. Find the absolute and relative change.

The absolute difference, or absolute change, is the new value minus the original value. The new value from 2015 is 108 students and the original value from 2014 is 120 students. So, the absolute difference is:


The absolute change is -12. The relative change will be the absolute difference divided by the initial value of 120 students:


To answer the question, the absolute change is -12 students and the relative change indicates a decrease of 10%. Notice that the absolute change is negative and this indicates a decrease in relative change.

EXAMPLE

In 2000, there were 5000 students enrolled in a local college. In 2010, there were 6250 students enrolled in the same college. What is the absolute change and the relative change?

The absolute difference, or absolute change, is the new value minus the original value. The new value from 2010 is 6250 students and the original value from 2000 is 5000 students. So, the absolute difference is:


The relative change is the absolute difference divided by the initial value of 5000 students:


To answer the question, the absolute change is 1250 students and the relative change indicates an increase of 25%. Notice that the absolute change is positive and this indicates an increase in relative change.