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Quartiles

The Second Quartile

We’ll come back to the music dataset in a bit, but let’s first practice on a small dataset.

Let’s begin by finding the second quartile (Q2). Q2 happens to be exactly the median. Half of the data falls below Q2 and half of the data falls above Q2.

The first step in finding the quartiles of a dataset is to sort the data from smallest to largest. For example, below is an unsorted dataset:

`$[8, 15, 4, -108, 16, 23, 42]$`

After sorting the dataset, it looks like this:

`$[-108, 4, 8, 15, 16, 23, 42]$`

Now that the list is sorted, we can find Q2. In the example dataset above, Q2 (and the median) is `15`

— there are three points below `15`

and three points above `15`

.

You might be wondering what happens if there is an even number of points in the dataset. For example, if we remove the `-108`

from our dataset, it will now look like this:

`$[4, 8, 15, 16, 23, 42]$`

Q2 now falls somewhere between `15`

and `16`

. There are a couple of different strategies that you can use to calculate Q2 in this situation. One of the more common ways is to take the average of those two numbers. In this case, that would be `15.5`

.

Recall that you can find the average of two numbers by adding them together and dividing by two.

We’ve included two small unsorted datasets named `dataset_one`

and `dataset_two`

.

We’ve also included, as a comment, the sorted version of the first dataset.

By looking at sorted version of `dataset_one`

, find the second quartile of the dataset and store it in a variable named `dataset_one_q2`

.

Find the second quartile of the `dataset_two`

and store it in a variable named `dataset_two_q2`

.

Remember to sort the dataset. It might help to write out the sorted dataset as a comment!

Since there are an even number of datapoints in this dataset, the second quartile will fall between two points. The second quartile will be the average of those two points.