In this video we’re going to talk a little bit more about Interquartile Range, which we denote as IQR and that’s what you’ll see later on in your lesson. IQR. If we look at a box plot, Ok? IQR is the difference between your Q one and your Q three. So we find it by taking our Q three and subtracting our Q one. So that means that it is all this data right in here. Right between those. So it’s the actual box of the boxplot between these two numbers.

And this represents the middle fifty percent of our data. So the numbers between Q one and Q three. Very simple to find.

So let’s try one. Ok, I have these numbers here. I already listed them in order for you. So we don’t have to worry about finding them in order in this one as we normally do. So before we can find our Interquartile Range, our IQR.

We need to find our Q one, Q two, and our Q three. So let’s do the Q two, which again, is called the what? Very good, our Median. So it’s right here, it’s nine. So this is the middle of our data points. So let’s find our Q one. And remember our Q one is the median of the first half of our data since we have two numbers left, that is right smack dab in the middle, that means we do our seven plus eight divided by two which is seven point five.

Let’s do the same thing over here with our Q three, which again is the median of the second half of the data. We have two left again, smack dab in the middle. Nine plus ten divided by two, nine point five. So again, how do we find our IQR?

Right, it’s taking Q three and subtracting Q one. So let’s do that. Our Q three again was nine point five. Our Q one was seven point five ...let’s color code this. So if I just subtract those two, I get two. So there’s our IQR for this data, it’s two. So if I had a box plot. Let’s draw one real quick here, let’s just worry about the box of it. Here’s my Q one and my Q three, remember that Interquartile Range is all of this in the middle here, this whole part of the box right here. And that has a difference of two. So the middle fifty percent of my data is within a range of two units. So that’s how you find the IQR based on a list of data.

Now if they happen to give you a box, it’s really simple, you find out this one, you find this one and you subtract them and that’s all it is. It’s the actual box of the box plot.