Welcome back to BOGObiology!
This tutorial is going to be a little different than usual.
Today, we're going to be doing some math and reviewing how to calculate percent change.
Percent change is a measure of how much something has changed over time.
It compares an older value with a newer one,
and it can also be called relative change, percent increase or percent decrease.
Percent change is useful across every branch of science because it allows us to put our data into context.
Having a basic understanding of how it works is also very useful in everyday life. Consider the following (fake) headlines...
"PARTICIPANTS LOST 25 LBS!"
"OUR STOCK PRICE SURGED BY $5!"
"ATHLETE WINS OLYMPIC GOLD AND SETS RECORD BY 1 SECOND!"
And, my least favorite after a year of pandemic... "500 NEW CORONAVIRUS CASES RECORDED TODAY!"
Not only do these sound like clickbait, but they also don't tell us very much.
In order to better understand each of these topics, we have to ask ourselves at least two more questions.
Number 1: "Is that a lot?"
And Number 2: "Is that good or bad?"
With the fake weight loss example, we don't know what patients weighed at the start of the experiment.
Did people weigh 400 lbs? Or did they weigh 100 lbs?
This is a key piece of information as we assess how effective this diet is likely to be.
Similarly, the starting price of our fictional stock will determine
whether a $5 increase is just a small blip, or whether it's truly a massive surge.
Percent change is also very useful in athletics.
Winning a gold medal is impressive no matter what!
But setting a record by 1 second is going to mean different things depending on how long the race was.
Was it a marathon, or was it a sprint?
We use a standard equation to calculate the size of a relative change?
Here are two versions of the same equation.
Obviously, you should use whichever one makes the most sense to you.
In the numerator, we are figuring out how much change has occurred.
Then we are comparing it in the denominator to the initial value or the starting value.
This can be a little confusing.
So, we're going to work through a few practical examples using some of our clickbait headlines from earlier.
We'll start with the diet example.
It claims that participants all lost 25 lbs, but we need some context.
We'll use two fictional patients:
One who weighed 400 lbs, and one who weighed 100 lbs at the start of the experiment.
We're going to use our standard equation, and we'll begin
by filling in the patients' starting weights in place of X1 in both A and B.
Since we know that each of these patients both lost 25 lbs on our fictional diet,
we can also figure out what their end weight was.
Then we can plug it into the equations.
375 for Patient A and 75 for Patient B.
From here, it's just simple math.
We combine the numbers in the numerator, divide it by the denominator,
and then multiply it by 100 to transform it into a percent.
Try pausing the video and see if you can finish the calculations yourself from here.
Patient A has lost about 6.25% of their bodyweight.
See if you can figure out how much Patient B lost.
Notice that both of our answers are negative.
This doesn't mean that the change it bad,
but it does mean that the value is decreasing over time.
Both of our fictional patients lost weight on this diet,
but a 25 lb weight loss is NOT safe for someone who only weighed 100 lbs to begin with.
This person would have lost a quarter of their bodyweight.
This is crucial context that was missing from the original headline,
and that was only revealed when calculating percent change.
Now see if you can calculate percent change for two stocks.
Their prices both increased by $5, but one was far more expensive to begin with.
Before you begin, definitely make sure all your units are consistent.
If we do out the math, we can see that option B is definitely a surge.
But option A? Not so much!
You can also use this same equation to calculate the final
or initial value if you know the percent change.
For instance, a conservation organization might set a goal
of increasing the population of an endangered species by a specific amount over a few years.
If the goal is to increase the population by 30%,
input 30 where the "C" goes.
Then add in other given values.
Here, you have the initial population.
The final population is the unknown, so that's what we're going to solve for.
Again, see if you can solve this yourself before you watch me do it.
If you do out the math, you'll find that
increasing a population of 10 by 30% results in 13 organisms at the end.
If you start with a population of 5000,
if you increase by 30%, you'll end up with a population of 6,500 organisms.
When it comes to ecology, a key takeaway is
that the larger your population is, the more organisms you can afford to lose.
If you have a small population, however,
losing just a few organisms can be a disaster.
That wraps up our first ever math tutorial on percent change!
Thanks again for watching and remember to like, comment and subscribe! Bye!