Box plot with plt.boxplot in Matplotlib - Step-by-Step Execution

Concept Flow - Box plot with plt.boxplot

Start with data array

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Call plt.boxplot(data)

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Calculate quartiles and median

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Calculate whiskers and outliers

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Draw box, whiskers, and points

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Show plot with plt.show()

This flow shows how matplotlib takes data, calculates statistics, draws the box plot, and displays it.

Execution Sample

Matplotlib

import matplotlib.pyplot as plt

data = [7, 15, 36, 39, 40, 41, 42, 43, 47, 49]
plt.boxplot(data)
plt.show()

This code creates and shows a box plot for the given data list.

Execution Table

Step	Action	Value/Result	Explanation
1	Input data	[7, 15, 36, 39, 40, 41, 42, 43, 47, 49]	Data list provided to boxplot
2	Calculate Q1 (25th percentile)	36.75	Lower quartile of data
3	Calculate Median (50th percentile)	40.5	Middle value of data
4	Calculate Q3 (75th percentile)	42.75	Upper quartile of data
5	Calculate IQR	6.0	Q3 - Q1 = 42.75 - 36.75
6	Calculate lower fence	27.75	Q1 - 1.5*IQR = 36.75 - 9
7	Calculate upper fence	51.75	Q3 + 1.5*IQR = 42.75 + 9
8	Determine whisker data points	36 (low), 49 (high)	Furthest data points within fence range
9	Identify outliers	7, 15	Data points outside fences
10	Draw box plot	Box from 36.75 to 42.75, median at 40.5, whiskers to 36 & 49, outliers at 7 & 15	Visual representation created
11	Show plot	Plot window opens	User sees the box plot
12	End	Execution complete	Plot displayed successfully

💡 All steps completed, box plot displayed with outliers at 7 and 15.

Variable Tracker

Variable	Start	After Step 2	After Step 3	After Step 4	After Step 5	After Step 6	After Step 7	After Step 8	After Step 9	Final
data	[7,15,36,39,40,41,42,43,47,49]	[7,15,36,39,40,41,42,43,47,49]	[7,15,36,39,40,41,42,43,47,49]	[7,15,36,39,40,41,42,43,47,49]	[7,15,36,39,40,41,42,43,47,49]	[7,15,36,39,40,41,42,43,47,49]	[7,15,36,39,40,41,42,43,47,49]	[7,15,36,39,40,41,42,43,47,49]	[7,15,36,39,40,41,42,43,47,49]	[7,15,36,39,40,41,42,43,47,49]
Q1	None	36.75	36.75	36.75	36.75	36.75	36.75	36.75	36.75	36.75
Median	None	None	40.5	40.5	40.5	40.5	40.5	40.5	40.5	40.5
Q3	None	None	None	42.75	42.75	42.75	42.75	42.75	42.75	42.75
IQR	None	None	None	None	6.0	6.0	6.0	6.0	6.0	6.0
Lower whisker	None	None	None	None	None	27.75	27.75	27.75	27.75	27.75
Upper whisker	None	None	None	None	None	None	51.75	51.75	51.75	51.75
Whisker points	None	None	None	None	None	None	None	[36,49]	[36,49]	[36,49]
Outliers	None	None	None	None	None	None	None	None	[7,15]	[7,15]

Key Moments - 3 Insights

Why is the median not the middle number in the data list?

The median is the middle value after sorting the data. In this example, the median is calculated as the average of the 5th and 6th values (40 and 41), resulting in 40.5, as shown in execution_table step 3.

What determines the length of the whiskers in the box plot?

Whiskers extend to the smallest and largest data points within 1.5 times the IQR from Q1 and Q3. This is shown in steps 6, 7, and 8 of the execution_table.

Why are there outliers in this box plot?

Outliers are data points outside the fences (27.75 to 51.75). 7 and 15 are below the lower fence, as identified in step 9.

Visual Quiz - 3 Questions

Look at the execution table, what is the value of Q3 after step 4?

A 40.5

B 37.25

C 42.75

D 49

💡 Hint

Check the 'Value/Result' column for step 4 in the execution_table.

At which step does the calculation of the interquartile range (IQR) occur?

A Step 5

B Step 7

C Step 3

D Step 9

💡 Hint

Look for the step where IQR is calculated in the execution_table.

If the data had a value of 60 added, how would the upper whisker change?

A It would increase to include 60

B It would stay the same at 51.75

C It would decrease

D It would become equal to Q3

💡 Hint

Refer to how whiskers are calculated as Q3 + 1.5*IQR in steps 7 and 8. 60 exceeds the new upper fence.

Concept Snapshot

plt.boxplot(data)
- Draws a box plot for the data list
- Calculates Q1=36.75, median=40.5, Q3=42.75
- Whiskers extend to 1.5*IQR=9 beyond quartiles (fences 27.75-51.75)
- Outliers (7,15) shown as points beyond whiskers
- Use plt.show() to display the plot

Full Transcript

This visual execution traces how matplotlib's plt.boxplot function works step-by-step. Starting with the input data list, it calculates the first quartile (Q1=36.75), median (40.5), and third quartile (Q3=42.75). Then it computes the interquartile range (IQR=6.0). The fences extend to 1.5 times the IQR (9.0) from Q1 and Q3 (27.75 to 51.75). Whiskers go to the extreme non-outlier points (36 and 49). Points outside (7, 15) are outliers. Finally, the box plot is drawn showing the box from Q1 to Q3 with a line at the median, whiskers, and outliers. The plot is displayed with plt.show(). This helps beginners see how the box plot summarizes data distribution visually.

Practice

1. What does the plt.boxplot() function primarily show about a dataset?

easy

A. The exact values of all data points

B. The spread and center of the data using quartiles

C. Only the average value of the data

D. The correlation between two variables

Solution

1. Step 1: Understand box plot purpose

   A box plot summarizes data distribution by showing quartiles and spread.

2. Step 2: Identify what plt.boxplot() displays

   This function creates a box plot that visualizes median, quartiles, and outliers.

3. Final Answer:

   The spread and center of the data using quartiles -> Option B

4. Quick Check:

   Box plot = Data spread and center [OK]

Hint: Box plots show spread and center, not individual points [OK]

Common Mistakes:

• Thinking boxplot shows all data points exactly
• Confusing boxplot with scatter plot
• Assuming boxplot shows correlation

2. Which of the following is the correct way to create a vertical box plot of data stored in a list named data using matplotlib?

easy

A. plt.boxplot(data, orientation='horizontal')

B. plt.boxplot(data, vertical=False)

C. plt.boxplot(data, vert=True)

D. plt.boxplot(data, vert='no')

Solution

1. Step 1: Check parameter for vertical boxplot

   The parameter to control vertical or horizontal is vert, which accepts True or False.

2. Step 2: Match correct syntax

   Using plt.boxplot(data, vert=True) creates a vertical box plot correctly.

3. Final Answer:

   plt.boxplot(data, vert=True) -> Option C

4. Quick Check:

   Use vert=True for vertical boxplot [OK]

Hint: Use vert=True for vertical boxplot in plt.boxplot [OK]

Common Mistakes:

• Using wrong parameter name like 'vertical'
• Passing string instead of boolean for vert
• Confusing orientation parameter which plt.boxplot doesn't use

3. What will be the output of the following code?

import matplotlib.pyplot as plt
import numpy as np
np.random.seed(0)
data = np.random.normal(0, 1, 100)
plt.boxplot(data, notch=True)
plt.show()

medium

A. An error because notch=True is invalid

B. A scatter plot of the 100 data points

C. A histogram of the data distribution

D. A box plot with a notch showing median confidence interval

Solution

1. Step 1: Understand the code

   The code generates 100 random normal values and plots a box plot with notch=True.

2. Step 2: Interpret notch=True effect

   The notch creates a narrow region around the median to indicate confidence interval visually.

3. Final Answer:

   A box plot with a notch showing median confidence interval -> Option D

4. Quick Check:

   notch=True adds median confidence notch [OK]

Hint: notch=True adds median confidence notch in boxplot [OK]

Common Mistakes:

• Thinking notch=True creates scatter or histogram
• Assuming notch=True causes error
• Confusing boxplot with other plot types

4. Identify the error in this code snippet that tries to plot a box plot:

import matplotlib.pyplot as plt
data = [1, 2, 3, 4, 5]
plt.boxplot(data, notch='yes')
plt.show()

medium

A. The 'notch' parameter should be a boolean, not a string

B. The data list must be a numpy array

C. plt.boxplot requires data to be a dictionary

D. plt.show() is missing

Solution

1. Step 1: Check the 'notch' parameter type

   The 'notch' parameter expects a boolean (True or False), not a string like 'yes'.

2. Step 2: Confirm data type and plt.show()

   Data as list is valid, and plt.show() is present, so no error there.

3. Final Answer:

   The 'notch' parameter should be a boolean, not a string -> Option A

4. Quick Check:

   notch must be True or False, not 'yes' [OK]

Hint: Use True/False for notch, not strings [OK]

Common Mistakes:

• Passing string instead of boolean for notch
• Thinking data must be numpy array
• Forgetting plt.show() (not error here though)

5. You have two datasets: data1 and data2. You want to compare their distributions side by side using box plots with different colors and horizontal orientation. Which code snippet correctly achieves this?

hard

A. plt.boxplot([data1, data2], vert=False, patch_artist=True, boxprops=[dict(facecolor='lightblue'), dict(facecolor='orange')])

B. plt.boxplot(data1, data2, vert=True, color=['red', 'green'])

C. plt.boxplot([data1, data2], orientation='horizontal', colors=['blue', 'orange'])

D. plt.boxplot([data1, data2], vert=True, patch_artist=True, boxprops=dict(facecolor='red'))

Solution

1. Step 1: Check data input format

   To plot multiple datasets side by side, pass a list of datasets: [data1, data2].

2. Step 2: Verify horizontal orientation and color options

   Use vert=False for horizontal boxplots, patch_artist=True to fill boxes with color, and boxprops to set facecolor.

3. Step 3: Evaluate options

   plt.boxplot([data1, data2], vert=False, patch_artist=True, boxprops=[dict(facecolor='lightblue'), dict(facecolor='orange')]) correctly uses these parameters. Options A, B, and D use invalid parameters or syntax. plt.boxplot([data1, data2], vert=True, patch_artist=True, boxprops=dict(facecolor='red')) is vertical, not horizontal.

4. Final Answer:

   plt.boxplot([data1, data2], vert=False, patch_artist=True, boxprops=[dict(facecolor='lightblue'), dict(facecolor='orange')]) -> Option A

5. Quick Check:

   Multiple data + vert=False + patch_artist for color [OK]

Hint: Use vert=False and patch_artist=True for colored horizontal boxplots [OK]

Common Mistakes:

• Passing datasets separately instead of as list
• Using wrong parameter names like 'orientation'
• Forgetting patch_artist=True to fill colors