1.4.1 Stat Percentiles and Cumulative Relative Frequency Graphs

Added: 2026-06-03

[00:00:00]in this video we'll look at percentiles a percentile is a way to report data and show what percentage of scores were less than some particular value you might be familiar with this in test scores for standardized tests like the SAT maybe you got your score report back and you saw that you were in say the 82nd percentile what that would mean is that you scored better than 82 percent of all of the other test takers so let's look at an example of how that works so let's say we have Jenny who scored an 86 on her test and the stem pop shows all of the other test scores of her classmates so we find the 86 that's involved there and then we count up how many people scored less than 86 so we do not include the 86 just all the values that are less than that if we do that there are 21 people in her class that scored less than 8 and 86 out of the 25 students total so if you do 21/25 you get 0.8 4 or 84% so Jenny scored better than 84% of her classmates which is another way to say that she's in the 84th percentile next we want to take a look at cumulative relative frequency graphs so cumulative just like if you were thinking of if you had a cumulative final exam that would mean that everything from the whole year would be on that test for a cumulative relative frequency graph it means you're going to be looking at certain outcomes plus all of the outcomes that occurred before then so here's an example where we look at the ages of the first 44 presidents when they are inaugurated and there were for example here two presidents that were between the ages of 40 and 44 when they were inaugurated and there were seven for example that were between the ages of 60 and 60 or so out of 44 so 2 out of 44 that's 4.5% 7 out of 44 that's 15.9% you're familiar with this we did this back in chapter 1 that's just the relative frequencies if we want to find the relative the cumulative relative frequencies what we'll do is we'll add in the previous values as well so here's where these numbers are coming from the there's still only two presidents that were between the ages of 40 and 44 when they were inaugurated but then there's seven that were between the ages of 45 and 49 so if we want the cumulative value that's the two from before plus the seven new ones which is nine total and then from 50 to 54 there's 13 of those so if we add in another 13 now we're at 22 total that are from 52 54 or younger when they were inaugurated so that's where these numbers here are coming from they're adding each of these previous values and then when we when we find their cumulative relative frequencies now are doing 2 out of 44 9 out of 44 instead of 7 out of 44 and so forth and notice that in a cumulative relative frequency by the time you get to the end it's going to add up to 100% there's now you have 100% of all of the data if we then plot all of these values so from 0 or sorry from 40 to 44 that's 4.5% and then when we get to 45 to 49 that's at 20.5% so that's where this point here is this is the roughly twenty point five percent instead of fifteen point nine percent so we're plotting these values along the y axis instead of these values and you'll see that well and at a hundred percent since that will be well the total will be a total of a hundred percent by the time we're done