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.

Practice

1. What does a box plot primarily show about a dataset?

easy

A. Only the average value of the data

B. The spread, median, and outliers of the data

C. The exact values of all data points

D. The correlation between two variables

Solution

1. Step 1: Understand box plot components

   A box plot shows the median line, the box representing the middle 50% of data, and whiskers for spread.

2. Step 2: Identify what it reveals

   It highlights the data spread, median, and any outliers beyond whiskers.

3. Final Answer:

   The spread, median, and outliers of the data -> Option B

4. Quick Check:

   Box plot = spread + median + outliers [OK]

Hint: Box plots show spread and outliers, not just averages [OK]

Common Mistakes:

• Thinking box plots show all data points exactly
• Confusing box plots with scatter plots
• Assuming box plots show correlation

2. Which of the following is the correct way to create a box plot for a pandas DataFrame named df?

easy

A. boxplot(df)

B. df.plot.boxplot()

C. df.boxplot()

D. df.box()

Solution

1. Step 1: Recall pandas box plot syntax

   The pandas DataFrame method to create a box plot is boxplot().

2. Step 2: Check each option

   df.boxplot() uses df.boxplot(), which is correct. df.plot.boxplot() is invalid syntax. boxplot(df) is not a pandas function. df.box() is invalid.

3. Final Answer:

   df.boxplot() -> Option C

4. Quick Check:

   Use df.boxplot() to plot box plots [OK]

Hint: Use df.boxplot() to create box plots in pandas [OK]

Common Mistakes:

• Using df.plot.boxplot() which is invalid
• Trying to call boxplot as a standalone function
• Using df.box() which does not exist

3. Given the following code, what will be the output type of ax?

import pandas as pd
import matplotlib.pyplot as plt

df = pd.DataFrame({
    'A': [1, 2, 5, 7, 9],
    'B': [2, 3, 5, 8, 10]
})
ax = df.boxplot()

medium

A. A matplotlib AxesSubplot object

B. A list of numbers

C. A pandas DataFrame

D. A matplotlib Figure object

Solution

1. Step 1: Understand df.boxplot() return type

   The boxplot() method returns a matplotlib AxesSubplot object representing the plot area.

2. Step 2: Check options against expected type

   The return type is a matplotlib AxesSubplot object. This is not a pandas DataFrame, not a list of numbers, and not a matplotlib Figure object.

3. Final Answer:

   A matplotlib AxesSubplot object -> Option A

4. Quick Check:

   df.boxplot() returns AxesSubplot [OK]

Hint: df.boxplot() returns a matplotlib Axes object [OK]

Common Mistakes:

• Expecting a DataFrame or list as output
• Confusing Figure and Axes objects
• Assuming no return value

4. What is wrong with this code snippet that tries to create a box plot grouped by a column?

import pandas as pd
df = pd.DataFrame({
    'Category': ['X', 'X', 'Y', 'Y'],
    'Value': [10, 15, 10, 20]
})
df.boxplot(column='Value', by='Category', groupby='Category')

medium

A. The argument 'groupby' is invalid for boxplot()

B. The 'by' argument should be 'groupby'

C. The 'column' argument should be a list, not a string

D. The DataFrame is missing numeric columns

Solution

1. Step 1: Check boxplot() arguments

   The pandas boxplot method accepts 'column' and 'by' arguments, but not 'groupby'.

2. Step 2: Identify invalid argument

   The code incorrectly uses 'groupby' which causes an error. 'by' is correct for grouping.

3. Final Answer:

   The argument 'groupby' is invalid for boxplot() -> Option A

4. Quick Check:

   Use 'by' to group, no 'groupby' argument [OK]

Hint: Use 'by' to group in boxplot(), not 'groupby' [OK]

Common Mistakes:

• Using 'groupby' instead of 'by' argument
• Passing column as list when string is allowed
• Thinking numeric columns are missing

5. You have a DataFrame df with columns "Group" and "Score". You want to compare the score distributions for each group side by side using box plots. Which code correctly achieves this?

hard

A. df.boxplot(by='Score', column='Group')

B. df.groupby('Group').boxplot(column='Score')

C. df.plot.box(by='Group', column='Score')

D. df.boxplot(column='Score', by='Group')

Solution

1. Step 1: Understand grouping in boxplot()

   To compare groups side by side, use boxplot() with column as the numeric data and by as the grouping column.

2. Step 2: Evaluate each option

   df.boxplot(column='Score', by='Group') correctly uses column='Score' and by='Group'. df.groupby('Group').boxplot(column='Score') tries to group then boxplot, which returns multiple plots, not side by side. df.plot.box(by='Group', column='Score') uses invalid syntax. df.boxplot(by='Score', column='Group') swaps column and by incorrectly.

3. Final Answer:

   df.boxplot(column='Score', by='Group') -> Option D

4. Quick Check:

   Use column=score and by=group for grouped boxplots [OK]

Hint: Use df.boxplot(column='Score', by='Group') for grouped box plots [OK]

Common Mistakes:

• Using groupby().boxplot() which plots separately
• Swapping column and by arguments
• Using invalid plot syntax