Box plot

A box plot shows data spread and outliers.

Box plot

A box plot summarises a distribution with five numbers: the box is the first and third quartile (Q1, Q3), the middle line the median, the whiskers reach up to the 1.5·IQR limit; points outside are outliers.

fig, ax = plt.subplots()
ax.boxplot([X[y == 0, 0], X[y == 1, 0], X[y == 2, 0]])
ax.set_xticks([1, 2, 3], ["setosa", "versicolor", "virginica"])

It is tidier than a histogram for comparing several groups side by side.

Computing outliers

The outliers the plot marks can be found by hand with the same rule. This decides which examples to examine in the cleaning step:

q1, q3 = np.percentile(x, [25, 75])
iqr = q3 - q1
aykiri = x[(x < q1 - 1.5 * iqr) | (x > q3 + 1.5 * iqr)]

The plot and the calculation should agree; if they don't, the percentile method usually differs.

Exercise Box and outliers

Draw a box plot of x and save it. Print the median, then the outliers by the 1.5·IQR rule, on separate lines.

Show example solution

import numpy as np
import matplotlib.pyplot as plt

x = np.array([12, 14, 15, 15, 16, 17, 18, 19, 40])

fig, ax = plt.subplots()
ax.boxplot(x)
fig.savefig("kutu.png")
print(np.median(x))
q1, q3 = np.percentile(x, [25, 75])
iqr = q3 - q1
print(x[(x < q1 - 1.5 * iqr) | (x > q3 + 1.5 * iqr)])

Test yourself

What does the line in the middle of the box show in a box plot?
- The median
- The mean
- The mode
- The standard deviation
Show answer

The median — A box plot is based on quartiles; the middle line is the 50th percentile.
Draw the groups as a box plot.
```
ax.____([a, b, c])
```
Show answer
```
ax.boxplot([a, b, c])
```
Match the box plot parts.

box

Between Q1 and Q3
middle line

Median
whisker

1.5·IQR limit
outlier point

Outlier

Next lesson: Summary - Visualization

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