This is the median of the upper half of the data set. It is also known as the 75th percentile because it marks the point where 75% of the data is below it. As mentioned above, Quartile divides the data into 4 equal parts. There is a separate formula for finding each quartile value, and the ... More on geeksforgeeks.org

"I can't seem to figure out how to do it using the formulas." The simplest explanation is "you really can't reconcile the two methods." This is because, when it comes to a "formula-based algorithm" (what you're trying to use), there's no universally agreed upon method for calculating the quartiles. Try it with a smaller, more obvious list: 1,2,3,4,5,6,7,8. The median is clearly 4.5, the first quartile is clearly 2.5, and the 3rd quartile is clearly 6.5. However, if you muck around with this (n+1)/4 and 3(n+1)/4 mess, you get some 2.25 and 6.75 for the locations of the two points. "Rounding" gives you neither correct quartile. "Rounding up" and "rounding down" don't, either. Neither do "round up for this quartile but round down for that one." The other possibility is this idea of a weighted average. For the 2.25th slot for Q1, this means we'd take 25% of the 2nd slot plus 75% of the third slot. 2x0.25 + 3x0.75 = 2.75. Some people say to reverse this. Take 75% of the 2nd slot plus 25% of the third slot. 2x0.75 + 3x0.25 = 2.25. But why not go further? Take the median of those two and you'll get your 2.50. What if we just did that to begin with? Take the median of the 2nd and 3rd slot, and we'll get 2.5! Hopefully this works with Q3, so we take the median of the 6th and 7th slots to get 6.5. That works! But what happens when we tweak our list? 1,2,3,4,5,6,7,8,9,10. (10+1)/4 = 2.75th slot for Q1. This means we take the median of the 2nd and 3rd slots again, getting 2.5. ...However, if you split the data in half, it's very obvious that 3 is the correct Q1. Indeed, for the 8.25th slot for Q3, we should have the median of 8 and 9, or 8.5. But this should also be 8 for Q3. So, we're losing consistency here. And that's because the definition of a quartile is far more important than calculating it via formulas. In particular, if you are using an (n+1)/4 rule, you're always going to have 4 possible results with your data: (n+1)/4 and 3(n+1)/4 both whole numbers. No problem. (n+1)/4 and 3(n+1)/4 both end in some x.5 and y.5. No problem. Take medians between the x and x+1 and y and y+1. (n+1)/4 and 3(n+1)/4 end in some x.25 and y.75. Switch the two above around. It's those last two points that will give inconsistencies in the (n+1)/4 and 3(n+1)/4 formulas you're given. You would need either a different formula or a different method to get consistency. In general, sticking to the "split the data in half, and work with medians on the two halves" is going to be a lot better in the long run. But even HERE, people can't agree universally if they should include the median of original list in BOTH halves of the list or if it should be removed (when this sort of thing happens). More on reddit.com

You are not right. Or, maybe you are. There are hundreds of different ways to define procedures for finding percentiles/quartiles. Here is a listing of some of the common ones you encounter. Therefore, it isn't really interesting to talk about "right" or "wrong" ways of finding them. However, in an intro stats course, make sure you understand the way your instructor wants you to use. One thing that is for certain is that this particular example used in this class is idiotic. It is pedagogically very important to separate the two ideas: The numbers representing the ranks of the data in order (1st, 2nd, 3rd, etc.), from The numbers in the data themselves. Confounding the two by using fake data that are the same as the rank orders is guaranteed to confuse 1/2 the students. In other words, in reality the 1st quartile isn't "(3+4)/2" in the example you provided, but the mean of the 3rd and 4th values in the data set ordered from smallest to largest. More on reddit.com

But why isn't the first quartile 5 instead of 4.5? But ... but, you do it on the sorted data. 4 5 3 2 3 -> 2 3 3 4 5 2 3 3 4 5 Q1 Med Q3 Actually, in many definitions of sample quartiles, the lower quartile IS the second observation. In R, for example, there are nine definitions of quantiles in the "quantile" function (implying nine ways of arriving at a lower quartile), plus the lower hinge in the five number summary (and in the boxplot). Of those ten possible 'quartile' definitions in R, four of them give the second observation when n=5. Only one of the ten gives the (n+1)/4th observation Don't assume some site on the internet is the last word on anything. More on reddit.com