Box plots in Pandas - Step-by-Step Execution

Concept Flow - Box plots

Start with DataFrame

↓

Select numeric column

↓

Calculate quartiles and median

↓

Calculate whiskers (min/max within 1.5*IQR)

↓

Identify outliers

↓

Draw box (Q1 to Q3) and median line

↓

Draw whiskers and plot outliers

↓

Display box plot visualization

The flow starts from data, calculates key statistics, identifies outliers, and then draws the box plot step-by-step.

Execution Sample

Pandas

import pandas as pd
import matplotlib.pyplot as plt

data = {'Scores': [55, 67, 45, 70, 90, 85, 100, 40, 60, 75]}
df = pd.DataFrame(data)
df.boxplot(column='Scores')
plt.show()

This code creates a box plot for the 'Scores' column in the DataFrame.

Execution Table

Step	Action	Calculation/Condition	Result/Output
1	Start with DataFrame	DataFrame with 'Scores' column	[55, 67, 45, 70, 90, 85, 100, 40, 60, 75]
2	Calculate Q1 (25th percentile)	Q1 = 56.25	56.25
3	Calculate Median (50th percentile)	Median = 67.5	67.5
4	Calculate Q3 (75th percentile)	Q3 = 82.5	82.5
5	Calculate IQR	IQR = Q3 - Q1 = 26.25	26.25
6	Calculate lower whisker limit	Lower limit = Q1 - 1.5*IQR = 56.25 - 39.375 = 16.875	16.875
7	Calculate upper whisker limit	Upper limit = Q3 + 1.5*IQR = 82.5 + 39.375 = 121.875	121.875
8	Identify whiskers	Min data >= 16.875 is 40, Max data <= 121.875 is 100	Whiskers at 40 and 100
9	Identify outliers	Values <16.875 or >121.875? None	No outliers
10	Draw box from Q1 to Q3	Box from 56.25 to 82.5	Box drawn
11	Draw median line	Median at 67.5	Median line drawn
12	Draw whiskers	Whiskers at 40 and 100	Whiskers drawn
13	Plot outliers	No outliers	No outliers plotted
14	Display plot	Show box plot	Box plot displayed

💡 All steps completed, box plot displayed successfully.

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
Q1	N/A	56.25	56.25	56.25	56.25	56.25	56.25	56.25	56.25	56.25
Median	N/A	N/A	67.5	67.5	67.5	67.5	67.5	67.5	67.5	67.5
Q3	N/A	N/A	N/A	82.5	82.5	82.5	82.5	82.5	82.5	82.5
IQR	N/A	N/A	N/A	N/A	26.25	26.25	26.25	26.25	26.25	26.25
Lower whisker limit	N/A	N/A	N/A	N/A	N/A	16.875	16.875	16.875	16.875	16.875
Upper whisker limit	N/A	N/A	N/A	N/A	N/A	N/A	121.875	121.875	121.875	121.875
Lower whisker	N/A	N/A	N/A	N/A	N/A	N/A	N/A	40	40	40
Upper whisker	N/A	N/A	N/A	N/A	N/A	N/A	N/A	100	100	100
Outliers	N/A	N/A	N/A	N/A	N/A	N/A	N/A	None	None	None

Key Moments - 3 Insights

Why is the lower whisker at 40 and not at the minimum value 40?

The lower whisker is the smallest data point greater than or equal to the lower limit (Q1 - 1.5*IQR). Since 40 is the minimum and it is above 16.875, the whisker is at 40 (see execution_table step 8).

Why are there no outliers plotted even though 40 seems far from Q1?

Outliers are points outside the whisker limits. Since 40 is above the lower limit 16.875, it is not an outlier (see execution_table step 9).

What does the box represent in the box plot?

The box shows the middle 50% of data between Q1 and Q3, with a line at the median (see execution_table steps 10 and 11).

Visual Quiz - 3 Questions

Look at the execution table, what is the value of the median at step 3?

A 82.5

B 52.5

C 68.5

D 70

💡 Hint

Check the 'Median' row at step 3 in the execution_table.

At which step does the condition for identifying outliers get checked?

A Step 7

B Step 9

C Step 5

D Step 12

💡 Hint

Look for the step mentioning 'Identify outliers' in the execution_table.

If the maximum score was 110 instead of 100, what would happen to the upper whisker?

A It would move to 110

B It would stay at 100

C It would move to 121.875

D There would be no upper whisker

💡 Hint

Recall that whiskers are the max data point within the upper limit (121.875), see execution_table step 8.

Concept Snapshot

Box plots show data spread using quartiles.
Box covers Q1 to Q3, with a line at median.
Whiskers extend to data within 1.5*IQR from quartiles.
Points outside whiskers are outliers.
Use pandas.DataFrame.boxplot() to create easily.

Full Transcript

Box plots visualize data distribution by showing quartiles and outliers. We start with a DataFrame, select a numeric column, and calculate Q1, median, and Q3. The interquartile range (IQR) is Q3 minus Q1. Whiskers extend to the smallest and largest data points within 1.5 times the IQR from the quartiles. Points outside these whiskers are outliers. The box plot draws a box from Q1 to Q3 with a line at the median, whiskers, and marks outliers. In the example, the 'Scores' column is used to create a box plot with no outliers. This step-by-step process helps understand how box plots summarize data spread and detect unusual values.