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📚 Python for Introductory Statistics
Chapters ▾
0. Why Learn Python?1. Introduction to Python2. Python Lists3. Python Syntax4. Python Loops5. Frequency Distributions and Graphs6. Measures of Center and Variation7. Measures of Position8. Discrete Probability Distributions9. Continuous Probability Distributions10. Confidence Intervals11. Hypothesis Testing12. Linear Regression and Correlation13. Analysis of Categorical Data14. Advanced Statistics TopicsAppendix 1: Python Installing StepsAppendix 2: Random Integer GeneratorAppendix 3: Counting, Permutations and CombinationsCode ReferencesResources

7.3 Box Plot

Watch demo video

Box plots (also called box-and-whisker plots or box-whisker plots) give a good graphical image of the concentration of the data. A box plot is constructed from five values: the minimum value, the first quartile, the median, the third quartile, and the maximum value.

Syntax

import matplotlib.pyplot as plt
plt.boxplot(x)

Example: The dataset below is scores of 20 students in a stat class. Construct a box plot.

81, 21, 53, 32, 80, 13, 26, 42, 35, 41, 14, 25, 87, 62, 46, 40, 32, 52, 85, 28, 17, 36, 83, 79, 18, 50, 17, 36, 36, 19 

import matplotlib.pyplot as plt


x = [81, 21, 53, 32, 80, 13, 26, 42, 35, 41, 14, 25, 87, 62, 46, 40, 
             32, 52, 85, 28, 17, 36, 83, 79, 18, 50, 17, 36, 36, 19]

plt.boxplot(x)    

plt.suptitle("Box Plot")
plt.xlabel("Test Scores")
Show expected output
Text(0.5, 0, 'Test Scores')
Vertical box plot of the 30 test scores, titled Box Plot with x-label Test Scores: the box runs from about 25 to 62 with the median line at 36 and whiskers reaching 13 and 87.

Example: The dataset below is scores of 20 students in a stat class. Construct a horizontal box plot. Horizontal box plot is useful for identifying the shape of the distribution.

81, 21, 53, 32, 80, 13, 26, 42, 35, 41, 14, 25, 87, 62, 46, 40, 32, 52, 85, 28, 17, 36, 83, 79, 18, 50, 17, 36, 36, 19 

import matplotlib.pyplot as plt


x = [81, 21, 53, 32, 80, 13, 26, 42, 35, 41, 14, 25, 87, 62, 46, 40, 
             32, 52, 85, 28, 17, 36, 83, 79, 18, 50, 17, 36, 36, 19]


plt.boxplot(x,vert=False)  # add vert=False 
plt.suptitle("Box Plot")
plt.xlabel("Test Scores")
Show expected output
Text(0.5, 0, 'Test Scores')
The same box plot of the 30 test scores drawn horizontally (vert=False): median 36, box from about 25 to 62, whiskers 13 to 87.

Example: Below is the list of ages of US Senators (2020). Write a program to draw a box plot.

81,81,80,80,80,80,78,78,78,77,77,75,75,74,74,74,73,72,72,71,71,71,71,70,70, 70,70,68,68,68,68,68,67,67,67,66,66,65,65,65,65,64,64,64,64,64,64,63,63, 63,63,62,62,62,62,62,61,61,61,60,60,59,59,59,59,59,59,59,59,58,58,57,57, 56,56,55,54,54,54,54,54,53,53,52,52,52,52,52,51,50,49,48,46,45,44,43,43, 43,42,41 

import matplotlib.pyplot as plt


x = [81,81,80,80,80,80,78,78,78,77,77,75,75,74,74,74,73,72,72,71,71,71,71,70,70,
        70,70,68,68,68,68,68,67,67,67,66,66,65,65,65,65,64,64,64,64,64,64,63,63,
        63,63,62,62,62,62,62,61,61,61,60,60,59,59,59,59,59,59,59,59,58,58,57,57,
        56,56,55,54,54,54,54,54,53,53,52,52,52,52,52,51,50,49,48,46,45,44,43,43,
        43,42,41]

plt.boxplot(x)

plt.suptitle("Box Plot")
Show expected output
Text(0.5, 0.98, 'Box Plot')
Vertical box plot of the 100 ages titled Box Plot: median 63, box from the mid-50s to about 70, whiskers from 41 to 81, no outliers.
import matplotlib.pyplot as plt


x = [81,81,80,80,80,80,78,78,78,77,77,75,75,74,74,74,73,72,72,71,71,71,71,70,70,
        70,70,68,68,68,68,68,67,67,67,66,66,65,65,65,65,64,64,64,64,64,64,63,63,
        63,63,62,62,62,62,62,61,61,61,60,60,59,59,59,59,59,59,59,59,58,58,57,57,
        56,56,55,54,54,54,54,54,53,53,52,52,52,52,52,51,50,49,48,46,45,44,43,43,
        43,42,41]

plt.boxplot(x,vert=False)

plt.suptitle("Box Plot")

plt.xlabel("Age")
Show expected output
Text(0.5, 0, 'Age')
The same box plot of the 100 ages drawn horizontally with x-label Age: median 63, box mid-50s to about 70, whiskers 41 to 81.

Outliers

Example: For the data below, construct a horizontal box plot to identify any outliers.

1, 2, 2, 3, 3, 3, 3, 4, 7, 9,25 

import matplotlib.pyplot as plt

x=[1, 2, 2, 3, 3, 3, 3, 4, 7, 9,25]

plt.boxplot(x,vert=False)  
plt.suptitle("Box Plot")
Show expected output
Text(0.5, 0.98, 'Box Plot')
Horizontal box plot of [1, 2, 2, 3, 3, 3, 3, 4, 7, 9, 25] titled Box Plot: the box sits between about 2.5 and 5.5, the upper whisker ends at 9, and 25 is drawn as a separate outlier point.

25 is identified as an outlier in the boxplot above marked with o. Any value below the left whisker or above the right whisker is considered an outlier.

Adapted from Python for Introductory Statistics, by Simon Aman (Truman College, City Colleges of Chicago), licensed under CC BY 4.0. Changes were made: reformatted as an accessible XYZ web edition with live in-browser code cells. License: CC-BY-4.0.