Quartiles and Interquartile Range 04:58 minutes

Video Transcript

Transcript Quartiles and Interquartile Range

"Many archers, who all shoot brilliantly, on a Medieval castle ground is where we lay our scene. From fierce competition break to new scrutiny, Where quartiles determine the archers' destinies."

Romeo has entered an archery competition devised by the King based on quartiles. The rules of the competition are a little bit different from the competitions Romeo usually enters. Upon hearing that Juliet lives in the castle, Romeo is trying to find a way they can finally be together. However, in order to avoid the punishments, Romeo has to understand quartiles and interquartile range.

Quartiles and interquartile range

(A) The archers in the 4th quartile range are rewarded by being automatically knighted and sent to look for the Holey Grail, (B) while the archers in the 1st quartile range have the unfortunate lot of being the ones upon whose heads the target apples will sit next year. (C) Anyone falling in the lower part of the interquartile range has to clean up after the festival. (D) and anyone in the upper part of the interquartile range gets to stay in the castle during the festival. That's what Romeo wants. Additionally, if the competition isn't very good and the interquartile range is greater than 10, then all the archers in the interquartile range must help with the festival clean up.

Using quartiles

One way to analyze data is to use quartiles, which is just a fancy way of saying the data is divided into quarters. The competition between the kingdom's brave archers has just ended! Let's see what fate has in store for Romeo and Juliet. In our data set, we have several archers who had to shoot 20 apples each and managed to hit between 0 and 20 apples. Boy, that looks messy. In order to split the data into quartiles, we first need to put the numbers in order and done.

Let's take a look at a few of the ways to split this data. For this method, you need to know how many data points you have, so count those first.19. Good. We first need to split the list in two equal halves. If there is an odd number of data points, as in the example, then the middle number, 8, becomes the median and is not included in either half. We'll call this Q2. Once we have two halves, we want to split these into further halves, giving us four sets of data with an equal number of data points in each set. Let's look at the first half of the list first. It has 9 elements, so the median will not be included in either quartile. Five is the median of the first half, so we'll call this Q1.

So our first quartile has the following data points: These poor souls will be the apple stands at next year's competition and our second quartile range has the following data points. Those archers have to clean up once the festival is done.Doing the same to the second half of the list gives us a median of 15. So our Q3 is 15 and the 3rd as well as the 4th quartile ranges.

The brave warriors in the 4th quartile range are automatically knighted and sent off in search of the Holey Grail. If there is an even number of data points, then we split the list in half and take the median of the two middle-most numbers. So, just to illustrate what we mean, let's say you have an even number of data points like in our 3rd quartile range. Splitting these up into sets with the same number of elements is easy: all we have to do is put two data points in each set. But where's the median of this data set including 4 values? As we said before, we split the list in half and take the median of the two middle-most numbers. In our case, the middle-most numbers are 11 and 13. The median between these two numbers is 11 plus 13 divided by two, so 12 is our median.

The interquartile range

Now that we understand how to split the data into quartiles, all the bean counter needs to figure out is whether or not anyone gets to stay in the castle. For this, we need the interquartile range. The interquartile range is found by subtracting Q1 from Q3.

So 10 is the interquartile range for our data. Whew! Not all the archers have to clean up after the festival! Since Romeo finished the competition with a score of 14, we can now safely say that he is in the upper portion of the interquartile range and gets to stay in the castle where he'll be close to his lady love! But, there's something fishy about one of the newly-knighted knights.

"Go hence, to have more talk of these sad things: Some shall be empower’d, and some employed: For never was a story of more woe Than this of Juliet and her Romeo."