Scatter plots in Pandas - Time & Space Complexity

Time Complexity: Scatter plots

O(n)

Understanding Time Complexity

We want to understand how the time to create a scatter plot changes as the data size grows.

How does plotting many points affect the time it takes?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import pandas as pd
import matplotlib.pyplot as plt

n = 1000  # example size

data = pd.DataFrame({
    'x': range(n),
    'y': range(n)
})

plt.scatter(data['x'], data['y'])
plt.show()

This code creates a scatter plot of n points using pandas and matplotlib.

Identify Repeating Operations

• Primary operation: Plotting each point on the scatter plot.
• How many times: Once for each of the n points in the data.

How Execution Grows With Input

As the number of points increases, the time to plot grows roughly in direct proportion.

Input Size (n)	Approx. Operations
10	10 operations (plotting 10 points)
100	100 operations (plotting 100 points)
1000	1000 operations (plotting 1000 points)

Pattern observation: The time grows linearly as the number of points increases.

Final Time Complexity

Time Complexity: O(n)

This means the time to create the scatter plot grows directly with the number of points.

Common Mistake

[X] Wrong: "Plotting a scatter plot takes the same time no matter how many points there are."

[OK] Correct: Each point must be drawn, so more points mean more work and more time.

Interview Connect

Understanding how plotting time grows helps you explain performance when working with large datasets in real projects.

Self-Check

"What if we used a sampling method to plot only a fraction of points? How would the time complexity change?"

Practice

1. What does a scatter plot primarily show in a pandas DataFrame?

easy

A. The relationship between two numeric columns

B. The frequency of a single categorical column

C. The sum of all numeric columns

D. The average value of a column over time

Solution

1. Step 1: Understand scatter plot purpose

   A scatter plot is used to visualize how two numeric variables relate to each other by plotting points on an x and y axis.

2. Step 2: Match with options

   Only The relationship between two numeric columns describes this relationship between two numeric columns, while others describe different chart types or summaries.

3. Final Answer:

   The relationship between two numeric columns -> Option A

4. Quick Check:

   Scatter plot = relationship between two numeric columns [OK]

Hint: Scatter plots always compare two numeric columns [OK]

Common Mistakes:

• Confusing scatter plots with bar charts
• Thinking scatter plots show single column frequency
• Assuming scatter plots summarize data instead of showing relationships

2. Which of the following is the correct syntax to create a scatter plot in pandas for columns 'height' and 'weight'?

easy

A. df.plot.scatter('weight', 'height')

B. df.scatter_plot('height', 'weight')

C. df.plot.scatter(x='height', y='weight')

D. df.plot.scatter(x=height, y=weight)

Solution

1. Step 1: Recall pandas scatter plot syntax

   The correct method is df.plot.scatter with x and y as column names in quotes.

2. Step 2: Check each option

   df.plot.scatter(x='height', y='weight') uses correct method and argument format. df.scatter_plot('height', 'weight') is invalid method. df.plot.scatter('weight', 'height') swaps x and y but is still valid syntax, but question asks for 'height' as x and 'weight' as y. df.plot.scatter(x=height, y=weight) uses variables without quotes causing error.

3. Final Answer:

   df.plot.scatter(x='height', y='weight') -> Option C

4. Quick Check:

   Correct syntax uses df.plot.scatter with x and y as strings [OK]

Hint: Use df.plot.scatter(x='col1', y='col2') with quotes [OK]

Common Mistakes:

• Using method scatter_plot instead of plot.scatter
• Passing column names without quotes
• Swapping x and y columns unintentionally

3. Given the code:

import pandas as pd
import matplotlib.pyplot as plt

data = {'age': [25, 30, 35, 40], 'income': [50000, 60000, 65000, 70000]}
df = pd.DataFrame(data)
df.plot.scatter(x='age', y='income')
plt.show()

What will the scatter plot show?

medium

A. A bar chart of age vs income

B. An error because plt.show() is missing

C. A line plot connecting age and income

D. Points showing income increasing with age

Solution

1. Step 1: Understand the code

   The DataFrame has 'age' and 'income' columns. The scatter plot plots 'age' on x-axis and 'income' on y-axis.

2. Step 2: Interpret the plot type and data

   Scatter plot will show points representing each person's age and income. Income increases as age increases, so points trend upward.

3. Final Answer:

   Points showing income increasing with age -> Option D

4. Quick Check:

   Scatter plot shows points, not bars or lines [OK]

Hint: Scatter plots show points, not bars or lines [OK]

Common Mistakes:

• Confusing scatter plot with bar or line plot
• Thinking plt.show() is optional and causes error
• Misreading which column is x or y

4. What is wrong with this code snippet to create a scatter plot?

df.plot.scatter(x=age, y='income')

medium

A. Scatter plots require plt.scatter, not df.plot.scatter

B. The variable age is not defined or quoted

C. plot.scatter does not exist in pandas

D. The y parameter should be numeric, not string

Solution

1. Step 1: Check the x parameter

   The x parameter should be the column name as a string, but age is unquoted, treated as a variable.

2. Step 2: Verify other parameters and method

   y='income' is correct as a string. plot.scatter is valid pandas method. So only x parameter is wrong.

3. Final Answer:

   The variable age is not defined or quoted -> Option B

4. Quick Check:

   Column names must be strings in plot.scatter [OK]

Hint: Always quote column names in plot.scatter [OK]

Common Mistakes:

• Passing column names without quotes
• Confusing pandas plot.scatter with matplotlib scatter
• Thinking y must be numeric type, not string

5. You have a DataFrame with columns 'temperature', 'sales', and 'day'. You want to create a scatter plot showing sales vs temperature, but color points by day of the week. Which approach is correct?

hard

A. Use df.plot.scatter(x='temperature', y='sales', c=df['day'].astype('category').cat.codes)

B. Use df.plot.scatter(x='temperature', y='sales', color='day')

C. Use df.plot.scatter(x='temperature', y='sales', c='day')

D. Use df.plot.scatter(x='temperature', y='sales', c=df['day'])

Solution

1. Step 1: Understand color parameter in scatter plot

   The c parameter expects numeric values for colors. The 'day' column is categorical (strings), so it must be converted to numeric codes.

2. Step 2: Check each option's color argument

   Use df.plot.scatter(x='temperature', y='sales', c=df['day'].astype('category').cat.codes) converts 'day' to category codes, which is correct. Use df.plot.scatter(x='temperature', y='sales', color='day') uses color='day' which is invalid. Use df.plot.scatter(x='temperature', y='sales', c='day') passes string 'day' which is invalid. Use df.plot.scatter(x='temperature', y='sales', c=df['day']) passes categorical strings directly, causing error.

3. Final Answer:

   Use df.plot.scatter(x='temperature', y='sales', c=df['day'].astype('category').cat.codes) -> Option A

4. Quick Check:

   Color values must be numeric codes for categorical data [OK]

Hint: Convert categorical to numeric codes for color in scatter [OK]

Common Mistakes:

• Passing categorical strings directly to color parameter
• Using color='day' instead of numeric codes
• Not converting categories before coloring