 So we can take enough to look at an important concept which we can call end-tiles and This is an important activity of mathematician Switches to take a look at a concept and ask yourself. Well, how can you generalize this? What can you do to make this apply to more things or to broaden our definition and one of the hallmarks of thinking? Mathematically is whether or not you get into the habit of asking How can I generalize an idea and in this particular case? We have this concept of the median and what does the median do? Well the median separates the data into two sets of equal size So the generalization maybe I can say divide these separate the data into a bunch of sets of equal size And so this is where our concept of end-tiles comes from we're going to separate the data into end sets of equal size Well, we could have seven tiles or nine tiles. There's actually only a few commonly used separations So one I could separate the data into two equal sets. We should call this a two tile or a duo tile But we just call it the median because we've already introduced that term But a generalization one of the common separations is to separate the data into four equal sets And this produces the core tiles We could also try separating it at ten equal sets. That's going to produce the deciles and then finally we might separate into 100 equal sets and this produces the percentiles as With the median the median is the value that separates the data into sets of equal size and Correspondingly the end tile is the value that separates the sets However, one important thing is that in common usage The end tile is usually used for the values in the equal sets as well How you speak influences how you think so it really is best if you talk about the end tile Producing or corresponding to the set and not to say that the values are in the end tile So for example, let's take a look at a bunch of data values Maybe it looks something like that and we'll note that the values here are actually in order Which is important because if they're not in order, we can't reasonably separate these sets and there's 12 values I'll count them up. There's 12 values all together. So I'm going to divide these values into sets of Four sets. I'm looking for the core tiles I'll divide it into four sets and that means that there's going to be three items in each set So this first set of three that first those first three values form a set I'll put a divider up the next set of three That'll be a next set the next set of three that'll be our next set and so there's my values there's my dividers and I'm going to have to determine what numbers actually produce those divisions and those are going to be the number that is between These two and as with the median will split the difference will find the number that's right in the middle So between these two values here That's going to be 3.5 between these two values here right in the middle 6.5 between these two values Well, they're exactly the same value So the number in the middle is the number itself and that gives us our core tiles And so we have our first core tile 3.5 this is the first quartile important to remember how you speak influences how you think the first quartile is the number and This corresponds to the values two two and three This is not the first quartile These are the values produced by the first quartile to get the values that correspond to the first quartile likewise, I have the second quartile 6.5 and again the quartile itself is the actual value and it corresponds to a set of data values for five and six Now note that the second quartile is also the median because it's divided the set into one two Quarters and one two quarters half the values are up here half the values are down here So the second quartile corresponds to the median the third quartile that third dividing point is going to be nine And that's going to correspond to the values seven seven and nine Now you'll notice that we've talked about the values in the first quartile values corresponding to the first quartile The values corresponding to the second the values corresponding to the third quartile But then we have said nothing about these values So sometimes we might say that they're the values in the fourth quartile But keep in mind that there's no actual fourth quartile value The quartiles are the dividing points and there's only three of them So there is no fourth quartile, but there are the remaining values