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In this lesson, learn how to plot boxplots by hand and using Python's matplotlib library.

Boxplots

We've spent this lesson building a boxplot by hand. Let's now look at how Python's Matplotlib library does it!

The `matplotlib.pyplot` module has a function named `boxplot()`. `boxplot()` takes a dataset as a parameter. This dataset could be something like a list of numbers, or a Pandas DataFrame.

```py
import matplotlib.pyplot as plt

data = [1, 2, 3, 4, 5]
plt.boxplot(data)
plt.show()
```

One of the strengths of Matplotlib is the ease of plotting two boxplots side by side. If you pass `boxplot()` a list of datasets, Matplotlib will make a boxplot for each, allowing you to compare their spread and central tendencies,

```py
import matplotlib.pyplot as plt

dataset_one = [1, 2, 3, 4, 5]
dataset_two = [3, 4, 5, 6, 7]
plt.boxplot([dataset_one, dataset_two])
plt.show()
```

Boxplots in Matplotlib

The final piece of a boxplot is the representation of outliers. An outlier is a point in the dataset that falls outside of the whiskers. Outliers are usually represented with a dot or an asterisk.

Outliers

Now that we've drawn the median, let's draw the edges of the box. The box extends to the first and third <a href="https://www.codecademy.com/courses/quartiles-quantiles-and-interquartile-range/lessons/quartiles/exercises/quartiles">quartile</a> of the dataset.

This visually splits the data into fourths. One-quarter of the data will fall outside of the box to the left. Another quarter of the data will fall between the left side of the box and the median line. A third quarter of the data falls between the median line and the right side of the box. And the last quarter of the data falls outside the box to the right.

By drawing the edges of the box using the first and third quartiles, the <a href="https://www.codecademy.com/courses/quartiles-quantiles-and-interquartile-range/lessons/interquartile-range/exercises/range-review">interquartile range</a> is visualized. The length of the box represents this commonly used descriptive statistic.

We can use NumPy's `quantile()` function to find the first and third quartile:

```py
dataset = [4, 8, 15, 16, 23]
first_quartile = np.quantile(dataset, 0.25) 
third_quartile = np.quantile(dataset, 0.75)
```


Interquartile Range

When making a box plot, the easiest place to start is the line that is inside the box. This line is the <a href="https://www.codecademy.com/courses/learn-statistics-with-python/lessons/median/exercises/introduction">median</a> of the dataset. Half of the data falls above that line and half falls below it.

We can find the median of a dataset by using NumPy's `median()` function.

```py
import numpy as np

dataset = [4, 8, 15, 16, 23]
dataset_median = np.median(dataset) 
# dataset_median stores the value 15
```


Median

Great work! Here are some of the major takeaways from boxplots:

* The box of a boxplot visualizes the median, first quartile, and third quartile of a dataset.
* The length of the box in a boxplot visualizes the interquartile range.
* The whiskers extend from the box 1.5 times the size of the interquartile range.
* Outliers are points that fall outside of the whiskers. They're represented by dots.
* Boxplots are especially useful for comparing the spread of multiple datasets.


Review

The whiskers of a boxplot display information related to the spread of the dataset. 

There are many different ways to plot the whiskers of a boxplot. You might see some boxplots where the whiskers extend to the minimum and maximum values. Some boxplots have whiskers that extend one standard deviation away from the mean of the data.

However, one of the most commonly used methods of drawing the whiskers is to extend them 1.5 times the interquartile range from the first and third quartile.

For example, let's say you had a dataset where the first quartile was `4` and the third quartile was `9`. The interquartile range for this dataset is `5`. 

The whiskers would extend 1.5 times the length of the IQR. In this case, that is `1.5 * 5`, or `7.5`.

We know the whiskers extend `7.5` units, but where do they start? They start at the edges of the box, or the first and third quartiles. In this case, the left whisker starts at the first quartile (`4`), and extend `7.5` units to the left. So the left whisker extends to `-3.5`. The right whisker starts at the third quartile (`9`) and extends to `16.5`.

<img src="https://content.codecademy.com/courses/statistics/boxplot/whiskers.svg">

One more small detail to note &mdash; the whiskers usually don't extend all the way to 1.5 times the IQR. Instead, they extend to the point closest to `1.5` times the IQR in the direction of the median. This means that instead of extending to `-3.5` and `16.5`, the whiskers would actually extend to the first point greater than `-3.5` and the first point less than `16.5`.

<img src="https://content.codecademy.com/courses/statistics/boxplot/short_whiskers.svg">



Whiskers

Boxplots are one of the most common ways to visualize a dataset. Like <a href="https://www.codecademy.com/courses/learn-statistics-with-python/lessons/histograms/exercises/introduction">histograms</a>, boxplots give you a sense of the central tendency and spread of the data.

Take a look at the boxplot on this page. This boxplot is visualizing a dataset containing the lengths of 9,975 songs. We'll highlight some of the features of the boxplot and will dig into them in more detail in this lesson:

* The line in the center of the box is the <a href="https://www.codecademy.com/courses/learn-statistics-with-python/lessons/median/exercises/introduction">median</a>.
* The edges of the box are the first and third <a href="https://www.codecademy.com/courses/quartiles-quantiles-and-interquartile-range/lessons/quartiles/exercises/quartiles">quartiles</a>. This makes the length of the box the <a href="https://www.codecademy.com/courses/quartiles-quantiles-and-interquartile-range/lessons/interquartile-range/exercises/range-review">interquartile range</a> &mdash; the middle 50% of your data.
* The whiskers of the boxplot extend to include most of the data. There are many different ways to calculate the length of the whiskers.
* Outliers are points that fall beyond the whiskers. Those points are represented with dots. In the boxplot we're showing, there are _many_ outliers.


A boxplot of a dataset of music song lengths.