In addition to being able to find a percent of data or a range of data, you can also find the percentile. Percentile is a specific amount of your variable. So, since earlier we were studying weights, a percentile would be a specific weight. Alright, and what does this percentile represent? What does this weight represent? It's representing that percent of data falls below that amount. What do I mean by that? Well, if you scored in the 25th percentile, it means 25% of test takers had a score lower than yours, below, below. And so we can utilize the empirical rule to also help us find percentiles. So let's go back to the same context problem again. We're still looking at the weight of women. We're still looking at the same mean. We're still looking at the same standard deviation. So let's just quickly label this normal curve using the exact same numbers that we did above in example one. Alright, so in this case, we're using 56, 82, 108, 134, 160, 186, and 212. Again, I want to just emphasize the fact we are looking at the same data, which means the horizontal axis of weights are still the same. And so what I want to do is I want to find what percentile is associated with 160 pounds. What percentile is associated with 160 pounds? So what we're going to do is go to 160 pounds, and then we think about what percentile means again. Percentile is emphasizing the idea of all the data that falls below 160 pounds. And so if we're thinking about falling below 160, are we going to shade to the left or to the right of 160? We are shading left. We are going to shade to the left. How do I actually find this area in pink? Well, let's just think about it logically, right? We know the mean is right smack down the middle. The mean is right smack down the middle. So, at least this pink part, shaded to the left of the middle, can you just tell me, based on basic ideas of cutting something in half, what percent of the data is that left-hand portion? Like we don't even need the empirical rule. 50%. And so what we really need to do is then figure out, well then, what is this right-hand side? And that's where the empirical rule can be further broken down. If you further break down the empirical rule, you would see that 68% is taking off both of these middle slices here. So if you divide 68 by two, you get 34 and 34, giving us then that from the mean to one standard deviation above, we are looking at 34% of our data. If you keep slicing up this graph based on one, two, three, three standard deviations above and below the mean, you will get all of these percentages. I'm not going to break down how the math occurred with that, but I just want you to understand each of these pink percentages are representing the area between each vertical slice. And so in this case, we are seeing that between the mean and one standard deviation above, we're looking at 34%. And so bringing that all together, 50% plus 34% is giving us 84%. And it's that 84% is why we then say 84 percentile. We would say that 160 pounds is the 84 percentile. It's representing the fact that 84% of women are 160 pounds or less. We can also go in the other direction where, instead of starting with a specific weight, we can actually start with a specific percentile. Start with a percentile and use that to estimate the women's weight. So in this case again, I want to remind you guys percentile is representing falling below a specific weight. And so when you are working with percentiles and you're thinking about falling below, what that emphasizes is you need to start this shading on the left. Why? So that as you are shading, all of the shading is happening to the left of a specific value. But the rub is, when do we actually get 16% of our area? Where do I stop on this horizontal line so that I only have shaded 16% of my area? And that is where, once again, the empirical rule, when broken down into each slice, gives us these wonderful little percentages. Notice that the percentage of data from the edge of the tail to three standard deviations, three standard deviations below the mean, is 0.15% of the data, nowhere near what we need. We need a big old 16%. But it's somewhere to start. So let's keep shading to the left. Let's keep shading to the left. And see now I'm looking at an area representing 0.15% of the data plus 2.35% of the data. So you've got to keep shading. You've got to keep shading from the left until we get to this next area, this next area of 13.5%. And ah, now have we gotten to 16% of the area? Yeah, yeah, we have. Yeah, we have. And I want you to see that where we stopped was one standard deviation below the mean to gain 16% of the area when starting shading on the left. We go all the way up to one standard deviation below the mean, and that's 108 pounds. So in this case, we would say that the 16 percentile is 108 pounds.