Quartiles | Lower Quartile, Median, and Upper Quartile | Math with Mr. J

[Music] welcome to math with mr j [Music] in this video i'm going to cover quartiles so the lower quartile the median and the upper quartile quartiles divide data sets into quarters simply put we break the data up into four equal parts the lower quartile will give us the 25th percentile so the 25 percent or one-fourth mark the median gives us the 50th percentile so the middle of our data and then the upper quartile will give us the 75th percentile the 75 percent or three-fourths mark all of this information helps us understand and interpret data quartiles are a building block for other topics involving data so an understanding of this will help you moving forward we have two examples that we're going to work through one example will have an odd number of numbers in the data set and the other will have an even number of numbers in the data set let's jump into our first example and in this example we're going to work with a data set with an odd number of numbers so let's jump into it and we need to start by ordering our data from least to greatest so ascending order now in this example the data is already in order but if you're working with a data set that's not in order make sure least to greatest or ascending order is the first thing you do the next step we need to find the median also referred to as q2 which means quartile 2 or the 50th percentile so this is going to be the middle of our data now for this example we have nine numbers in our data set so the middle is going to be the fifth number that's going to give us four numbers on the left and four numbers on the right so the fifth number is this eight right here that's going to be our median so let's put 8 for quartile 2 or the 50th percentile or the median now that's the middle point so what we need to do now we need to find the median of the lower half and the median of the upper half the median or middle of the lower half is going to give us the lower quartile and the median of the upper half or middle of the upper half is going to be the upper quartile so let's take a look at the lower half first and we have four numbers here so we need to find the middle so we have an even number of numbers within that lower half we have four numbers so we don't have a specific number sitting directly in the middle so we're going to have to take a look at the middle two numbers the two and the four right here now we need to find what's directly in between that 2 and 4. now we can think this through and we know 3 is in between 2 and 4. but sometimes it's not going to be that easy to figure out so we need to do it mathematically i'll show you how to do that as well and we'll see if we still get three so what we need to do if we need the median in between two numbers we find the average so we need to add then divide by two so we have two plus four and then divide by two that's going to give us our average so two plus four is six and six divided by two gives us three so we still got three so three is our quartile one or lower quartile 8 is our q2 to recap so our median and now we need to end with finding our upper quartile so we'll take a look at the upper half and we have four numbers here so an even number of numbers so we need to take a look at the midpoint or middle of our two middle numbers here so what's going to be in between 10 and 14. so let's find the average between those two numbers and that's going to give us the median of that upper half so we do 10 plus 14 and we divide by 2 to find the average so 10 plus 14 is 24 and 24 divided by 2 is going to give us 12. so 12 is going to be our upper quartile so let's split this data set into quarters or four equal pieces to give you a visual of splitting this up so we know our 25th percentile or lower quartile is at 3 which is right in between 2 and 4. so i'm going to draw a line our median or 50th percentile is this 8 right here so let's draw a line and then our upper quartile or 75th percentile is in between the 10 and 14 at 12. so you can see that we have 1 two three and four equal pieces that's what quartiles are we split our data set into four equal pieces now that we know how to find the lower quartile median and upper quartile of a data set with an odd number of numbers we're going to take a look at a data set with an even number of numbers so let's jump into it in this example we're going to work with a data set with an even number of numbers and we need to start by ordering our data from least to greatest so ascending order in this example we are already in order but if you're working with some numbers that are out of order make sure you start with ordering those numbers from least to greatest so let's move on to step two which is find the median now we have eight numbers within this data set so we're going to have four on the left and four on the right that's going to give us our middle it's going to be in between the 21 and the 28. so we need to find the middle between those two numbers and we can do that by finding the average so let's come down to where it says q2 which stands for quartile 2 which is the same thing as the median it's the 50th percentile so to find the average we need to add those numbers 21 plus 28 and then divide by 2. so 21 plus 28 gives us 49 and 49 divided by 2 is going to give us 24 and 5 10 or 24 and a half that's going to be our median that's the middle point of our data set there so once we have our median we need to find the median of the lower half and median of the upper half the median or middle of the lower half is going to be the lower quartile and then the median or middle of the upper half is going to be the upper quartile so let's do the lower half first so the lower four numbers we need to find the middle of those lower four numbers and since we have an even number of numbers there we don't have a number sitting directly in the middle so we're going to need to take a look at the two numbers in the middle and find what's in between that's going to give us our median again because we don't have one specific number sitting in the middle there so we need to take a look at the 2 in the middle and find what's in between and just like the median we can do that by finding the average or in the case of this one we can probably think it through and we know that 16 and a half is in between 16 and 17. but let's solve it mathematically as well so again average add 16 plus 17 and then divide by 2. so 16 plus 17 is going to give us 33 divided by 2 and we get 16 and 5 10 or 16 and a half that's going to give us our lower quartile so that's the 25 mark within our data set there the 25th percentile so once we have that we can do the upper quartile so let's take a look at the upper half and find the middle or median of that upper half now we have four numbers again an even number of numbers so we're not going to have one specific number sitting in the middle we're going to take a look at the two middle numbers which 31 and 39 and find the midpoint between those two that's going to give us our median of that upper half and we can do that by finding the average so add 31 plus 39 divided by 2. 31 plus 39 is going to give us 70. 70 divided by 2 gives us 35. so 35 is going to be the upper quartile it's the 75 percent mark within our data the 75th percentile so those are our quartiles the lower quartile is 16 and a half that's the 25th percentile then we have the median which is 24 and a half that's the 50th percentile the middle of our data set and then for our upper quartile we have 35 so that's the 75th percentile i'm going to draw some lines within our data set there so we can visualize where these quartiles are and how it breaks our data into four equal parts so 16 and a half is going to be right here right in between that's 16 and 17 that we talked about earlier the median which is the middle point is right here in between the 21 and 28 like we talked about earlier and then we have our upper quartile in between the 31 and the 39 so you can see that we have 1 2 three and four equal pieces this line right here represents the 25th percentile this line is the 50th and then this is the 75th so there you have it there's how you find the lower quartile the median and the upper quartile i hope that helped thanks so much for watching until next time peace