Box Plots

A box plot (or box-and-whisker plot) summarizes the distribution of a numeric variable using five key statistics - the minimum, first quartile, median, third quartile, and maximum - making it an efficient way to spot spread, skewness, and outliers at a glance.

Anatomy of a Box Plot

Box - spans from the first quartile (Q1) to the third quartile (Q3), representing the middle 50% of the data (the interquartile range, or IQR)
Line inside the box - marks the median (Q2)
Whiskers - extend to the smallest and largest values within 1.5 times the IQR from the box
Points beyond the whiskers - plotted individually as potential outliers

The IQR and Outlier Rule

IQR = Q3 - Q1
Lower bound = Q1 - 1.5 * IQR
Upper bound = Q3 + 1.5 * IQR

Any data point falling outside these bounds is typically flagged as a potential outlier.

Plotting in Python

import matplotlib.pyplot as plt

plt.boxplot(data, vert=True, patch_artist=True)
plt.ylabel("Value")
plt.title("Box Plot")
plt.show()

Comparing Groups

Box plots are especially useful for comparing distributions across multiple groups side by side - for example, comparing exam scores across several different classes in a single chart.

Box plots hide the underlying shape of the distribution (like whether it's bimodal) - pairing a box plot with a histogram often gives a more complete picture of the data.

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