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In this lesson, you will learn how to calculate the interquartile range of a dataset.

Interquartile Range

Nice work! You can now calculate the Interquartile Range of a dataset using R. The main takeaway of the IQR is that it is a statistic, like the range, that helps describe the spread of the center of the data. 

However, unlike the range, the IQR is robust. A statistic is robust when outliers have little impact on it. For example, the IQRs of the two datasets below are identical, even though one has a massive outlier.

```r
dataset_one = c(6, 9, 10, 45, 190, 200) # IQR is 144.5
dataset_two = c(6, 9, 10, 45, 190, 20000000) # IQR is 144.5
```
By looking at the IQR instead of the range, you can get a better sense of the spread of the _middle_ of the data.

The interquartile range is displayed in a commonly-used graph &mdash; the box plot.

<img src="https://content.codecademy.com/courses/statistics/quantiles/boxplot.png" alt="A box plot">

In a box plot, the ends of the box are Q1 and Q3. So the length of the box is the IQR.


Review

In the last exercise, we calculated the IQR by finding the quartiles using R and finding the difference ourselves. The stats library has a function that can calculate the IQR all in one step.

The `IQR()` function takes a dataset as a parameter and returns the Interquartile Range.

```r
dataset = c(4, 10, 38, 85, 193)
interquartile_range = IQR(dataset)
```


IQR in R

The interquartile range is the difference between the third quartile (Q3) and the first quartile (Q1). If you need a refresher on quartiles, you can take a look at our <a href="https://www.codecademy.com/courses/quartiles-quantiles-and-interquartile-range-r/lessons/quartiles-r/exercises/quartiles">lesson</a>. 

For now, all you need to know is that the first quartile is the value that separates the first 25% of the data from the remaining 75%.

The third quartile is the opposite &mdash; it separates the first 75% of the data from the remaining 25%.

<img src="https://content.codecademy.com/courses/statistics/quantiles/interquartile.svg" alt="The interquartile range of the dataset is shown to be between Q3 and Q1.">

The interquartile range is the difference between these two values.

Quartiles

One of the most common statistics to describe a dataset is the _range_. The range of a dataset is the difference between the maximum and minimum values. While this descriptive statistic is a good start, it is important to consider the impact outliers have on the results:

<img src="https://content.codecademy.com/courses/statistics/quantiles/outliers.svg" alt="A dataset with some outliers.">

In this image, most of the data is between `0` and `15`. However, there is one large negative outlier (`-20`) and one large positive outlier (`40`). This makes the range of the dataset `60` (The difference between `40` and `-20`). That's not very representative of the spread of the majority of the data!

The _interquartile range_ (IQR) is a descriptive statistic that tries to solve this problem. The IQR ignores the tails of the dataset, so you know the range around-which your data is centered. 

In this lesson, we'll teach you how to calculate the interquartile range and interpret it.
