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.