Understanding the Lower Quartile | Math Mr. J

In this video I'm going to specifically be covering the lower quartile. This is going to give us a better understanding of what the lower quartile is and represents. It's also going to give us a better understanding of quartiles in general. Now quartiles divide datasets into quarters or four equal parts. The lower quartile is going to be the 25 percent mark within our data. So the 25th percentile or one-fourth mark. Let's jump into our example to see exactly what this means and looks like. So we have nine numbers within our dataset here. And the first thing we want to always do is put the data in order from least to greatest. Also known as ascending order. In this case we are already in order. So we can move on to the next step which is finding the median. This is the middle of our data. The 50th percentile. Since we have nine numbers we're going to have four on the left and four on the right. And the number in the middle is our median. So this eight right here. This is our median. So our median equals eight. Once we have that we can find our lower quartile. Now we need to take a look at the lower half of our data. So these four numbers right here. The middle or median of this lower half is going to be the lower quartile. Since we have four numbers in our lower half we will not have one specific number sitting in the middle. We will have to take a look at the middle two numbers and find what is in between. And we'll do that by finding the average between them. Our middle two numbers are two and four. Two and four here. Now this one we can figure out without finding the average. Because we know three is in between two and four. Some problems are not going to be as simple as this though. So let's figure it out mathematically as well so we know how to do it. To find the average we need to add those numbers and divide by two. So I'm going to put Q1 down here equals. Now Q1 stands for quartile one. It's the same as lower quartile. So they mean the same thing. So lower quartile 25th percentile and Q1 all mean the same thing. So let's find the average. Two plus four. We're adding the two numbers and then dividing by two. So two plus four is six. Divided by two and we get three. The same thing we said earlier but here again we figured it out mathematically. So our lower quartile is three. This means that 25 percent of our data is less than three. And 75 percent is greater than three. So I'm going to make some marks in our data to help us visualize and understand what this all means. So to recap our median was eight. The middle number. So right here. This splits our data in half. Now our lower quartile was three. So that's going to be right here. And without going into detail this will be covered in another video. Our upper quartile is going to be between 10 and 14 right there. So those are our quartiles. We split our data into four equal groups. One. Two. Three. And four. So our focus was on the lower quartile which is right here. So to the left of that lower quartile we have 25 percent of our data. And to the right we have 75 percent of our data. And that lower quartile is the exact 25 percent mark or the 25th percentile. So there you have it. There's an explanation of the lower quartile. I'll add a link to the upper quartile and some other quartile videos I have down in the description. I hope that helped. Thanks so much for watching. Until next time. Peace.