In this video we’re going to talk about the Interquartile Range again, the IQR. Remember that the IQR represents the middle fifty percent of your data given. So it talks about the spread of that data, ok? If it’s, if the IQR is pretty large, you know the data is really spread out, that middle part is really spread out. If it’s small, it’s really close together.

So let’s try to find our IQR for this one. This is our average SAT scores for all of these different schools, entrance exam scores. So, again, before we can find IQR, we have to find our Q one, our Q two and our Q three.

Easiest one to find right off the bat, remember, is our Q two and what’s that called? Right. It’s called the Median of our set of data. Now this set of data is already in order for us. Remember, when you have to find the median of these, it has to be in order from least to greatest. So it already is that. So let’s go ahead and find this. All right so since we have two left over, we have to do our average of the two, nineteen fifteen plus nineteen thirty divided by two will give us nineteen twenty-two point five.

All right, let’s try to find our Q one now. Remember the Q one is the median of the first half, so let’s find the median of the first half. We’re down to two again which means it’s right here in the middle. Seventy ninety five plus eighteen o five divided by two gives me eighteen hundred.

So let’s find Q three which is the median of this bottom half. Let’s go ahead and do that one as well. Down to two again which means it’s right in the middle. Nineteen sixty five plus twenty fifteen divided by two gives me nineteen ninety as my Q three.

Now that we know those, we can find our IQR which again is the Q three minus Q one which is nineteen ninety minus eighteen hundred and that gives us one ninety. So our IQR, our Interquartile range is one hundred ninety points, so that’s pretty high, so our spread of our middle spread has a good bit of data between it.

So next what we’re going to do is we’re going to find the standard deviation with the same set of data. So if our standard deviation and we’re going to use the same set of data that we did in the previous, the first part of the video and a little notation here so you guys understand what’s being said up here, X of I represents the score, the SAT score for that particular school. X bar is the mean score and you did that earlier in the lesson and you got nineteen ten and then later on you’re going to see this little goofy looking E sign which means SUM, meaning add up the numbers.

So what we’re going to do first is we’re going to fill out this column right here. And what we’re going to do is you take, we’re going to do this exactly. We’re going to take this score, seventeen sixty, you’re going to subtract the mean, nineteen ten, and that’s going to give you negative one fifty. And as you can see it here, I’ll reveal it here, there’s that mean score right there - negative one fifty. Now what I’m going to do with that next, is I’m going to square it, right? Because that’s what that is here, square, I’m going to square that number and it’s going to give me twenty-two thousand, five hundred. So what I want you to do now is I want you to fill out this column by taking this number minus our nineteen ten, and then after you get the number in here, square it and put the number in this last column.

So go ahead and pause the video now and fill out the rest of this form.

All right now that you’re back, I’m going to reveal all of these scores because you should have filled these out. I’m just going to pull these over here. Ok? So check your work. Make sure that you got all these numbers here. All right. Now here’s all of the numbers if you squared those numbers. In this middle column. Make sure that your chart looks exactly like mine.

All righty. Let’s move on. So now we’re going to actually work towards our standard deviation. The first thing we need to do is we need to find the Sum, here’s that goofy little E looking thing of our last column here, that says X of I minus X bar squared. So we’re going to find that sum. So right now, pause the video, add all these numbers up here for me and then start the video again when you’re ready.

All right. You’re back. That means you summed it up. That means our SUM that we should have gotten was two thirteen twenty-two five, so, two hundred thirteen thousand, two hundred twenty-five should have been that sum. Now the next thing we’re going to do is we’re going to take our SUM and we’re going to divide it by N or the number schools that we have here so the number of numbers we have here, which in this case our N is twenty. So we’re going to take two hundred thirteen thousand two hundred twenty-five and divide it by twenty. And that will give us ten sixty-six one point two five, so we have ten thousand six hundred sixty one point two five. Next, our last step.

We have to take the square root of all of this meaning we’re going to take the square root of ten thousand six hundred sixty one point two five and that will give us one o three point three and this number is actually our standard deviation because the standard deviation equals this equation up here, which is the square root of the SUM of the squares of the difference divided by the number and that is what we said is one hundred three point three. Now as we talked about with the IQR it represents the spread of data. Last section, we also talked about the spread of data for a standard deviation. So right now one standard deviation is one hundred three point three points away from the mean. So that’s decently high, so we know that our one standard deviation away to the right and to the left is going to be anywhere from one hundred three point three points from the Mean to the right or to the left.