Why scatter plots show relationships in Matplotlib - Challenge Your Understanding

Challenge - 5 Problems

❓ Predict Output

intermediate

What is the output of this scatter plot code?

Look at the code below that creates a scatter plot. What will the plot show about the relationship between x and y?

Matplotlib

import matplotlib.pyplot as plt
x = [1, 2, 3, 4, 5]
y = [2, 4, 6, 8, 10]
plt.scatter(x, y)
plt.show()

A A scatter plot showing points in a straight line going up, indicating a positive linear relationship.

B A scatter plot showing points randomly scattered with no clear pattern.

C A scatter plot showing points in a straight line going down, indicating a negative linear relationship.

D A scatter plot showing points clustered at the origin with no spread.

💡 Hint

Look at how y changes as x increases.

The y values are exactly twice the x values, so the points form a straight line going up. This shows a positive linear relationship.

❓ data_output

intermediate

How many points are plotted in this scatter plot?

Given the data below, how many points will appear in the scatter plot?

Matplotlib

import matplotlib.pyplot as plt
x = [5, 3, 9, 1, 7]
y = [10, 6, 18, 2, 14]
plt.scatter(x, y)
plt.show()
num_points = len(x)

A 3

B 4

C 5

D 6

💡 Hint

Count the number of elements in the x list.

There are 5 elements in the x list, so 5 points will be plotted.

❓ visualization

advanced

Which scatter plot shows a negative relationship?

Below are four scatter plots created from different data sets. Which plot shows a negative relationship between x and y?

Matplotlib

import matplotlib.pyplot as plt
import numpy as np

fig, axs = plt.subplots(2, 2, figsize=(8, 6))

# Plot A: Positive linear
x = np.arange(10)
y = 2 * x + 1
axs[0, 0].scatter(x, y)
axs[0, 0].set_title('A')

# Plot B: Negative linear
x = np.arange(10)
y = 10 - x
axs[0, 1].scatter(x, y)
axs[0, 1].set_title('B')

# Plot C: No relationship
x = np.random.rand(10)
y = np.random.rand(10)
axs[1, 0].scatter(x, y)
axs[1, 0].set_title('C')

# Plot D: Clustered points
x = np.ones(10)
y = np.linspace(0, 5, 10)
axs[1, 1].scatter(x, y)
axs[1, 1].set_title('D')

plt.tight_layout()
plt.show()

A Plot A

B Plot C

C Plot D

D Plot B

💡 Hint

Look for points that go down as x increases.

Plot B shows y decreasing as x increases, which is a negative linear relationship.

🧠 Conceptual

advanced

Why do scatter plots help show relationships between variables?

Which explanation best describes why scatter plots are useful to see relationships between two variables?

A Because scatter plots show individual data points, making it easy to see patterns like trends or clusters.

B Because scatter plots only show averages, hiding individual differences.

C Because scatter plots connect points with lines to show exact changes over time.

D Because scatter plots use bars to compare categories clearly.

💡 Hint

Think about what you see when you look at a scatter plot.

Scatter plots display each data point, so you can see how variables relate by spotting patterns or groupings.

🔧 Debug

expert

What error does this scatter plot code produce?

Look at the code below. What error will occur when running it?

Matplotlib

import matplotlib.pyplot as plt
x = [1, 2, 3]
y = [4, 5]
plt.scatter(x, y)
plt.show()

A TypeError: 'list' object is not callable

B ValueError: x and y must be the same size

C SyntaxError: invalid syntax

D No error, plot will display correctly

💡 Hint

Check if x and y have the same number of elements.

The x list has 3 elements but y has 2, so matplotlib raises a ValueError about size mismatch.

Practice

1. What is the main reason we use scatter plots in data science?

easy

A. To sort data in ascending order

B. To see how two variables relate to each other

C. To calculate the average of a dataset

D. To create a list of unique values

Solution

1. Step 1: Understand the purpose of scatter plots

   Scatter plots show points representing two variables on a graph to visualize their relationship.

2. Step 2: Compare options with scatter plot use

   Calculating averages, sorting, or listing unique values are not visual tasks done by scatter plots.

3. Final Answer:

   To see how two variables relate to each other -> Option B

4. Quick Check:

   Scatter plots show relationships = C [OK]

Hint: Scatter plots show points for two variables to find relationships [OK]

Common Mistakes:

• Confusing scatter plots with bar charts
• Thinking scatter plots calculate statistics
• Believing scatter plots sort data

2. Which of the following is the correct way to create a scatter plot using matplotlib?

easy

A. plt.scatterplot(x, y)

B. plt.plot(x, y, 'scatter')

C. plt.bar(x, y)

D. plt.scatter(x, y)

Solution

1. Step 1: Recall matplotlib scatter plot syntax

   The correct function to create scatter plots in matplotlib is plt.scatter(x, y).

2. Step 2: Check other options for correctness

   plt.plot with 'scatter' is invalid, plt.bar creates bar charts, plt.scatterplot does not exist in matplotlib.

3. Final Answer:

   plt.scatter(x, y) -> Option D

4. Quick Check:

   Correct scatter plot function = D [OK]

Hint: Use plt.scatter(x, y) to plot scatter plots in matplotlib [OK]

Common Mistakes:

• Using plt.plot with wrong style
• Confusing bar charts with scatter plots
• Trying non-existent functions like plt.scatterplot

3. What will the following code show?

import matplotlib.pyplot as plt
x = [1, 2, 3, 4, 5]
y = [2, 4, 6, 8, 10]
plt.scatter(x, y)
plt.show()

medium

A. A scatter plot showing points forming a straight line going up

B. A scatter plot with points randomly scattered with no pattern

C. A bar chart with bars increasing in height

D. An error because plt.scatter needs labels

Solution

1. Step 1: Analyze the data points

   x and y values increase proportionally: y is 2 times x, so points lie on a straight line.

2. Step 2: Understand scatter plot output

   Scatter plot will show points aligned diagonally upwards, not random or bars, and no error occurs without labels.

3. Final Answer:

   A scatter plot showing points forming a straight line going up -> Option A

4. Quick Check:

   Proportional points form line = B [OK]

Hint: Check if y changes proportionally with x for line pattern [OK]

Common Mistakes:

• Thinking scatter plots create bar charts
• Expecting error without labels
• Assuming points are random without checking data

4. The code below is intended to plot a scatter plot but shows an error. What is the problem?

import matplotlib.pyplot as plt
x = [1, 2, 3]
y = [4, 5]
plt.scatter(x, y)
plt.show()

medium

A. plt.scatter cannot plot integers

B. plt.scatter requires labels before plotting

C. x and y lists have different lengths

D. plt.show() is missing

Solution

1. Step 1: Check the lengths of x and y

   x has 3 values, y has 2 values; scatter plot needs equal length lists for x and y.

2. Step 2: Verify other options

   Labels are optional, integers are valid, plt.show() is present, so these are not errors.

3. Final Answer:

   x and y lists have different lengths -> Option C

4. Quick Check:

   Equal length x and y needed = A [OK]

Hint: Ensure x and y lists have same length before plotting [OK]

Common Mistakes:

• Thinking labels are mandatory
• Believing plt.scatter can't plot integers
• Forgetting to check list lengths

5. You want to show a negative relationship between two variables using a scatter plot. Which data and code will best show this?

hard

A. x = [1, 2, 3, 4]; y = [10, 8, 6, 4]; plt.scatter(x, y)

B. x = [1, 2, 3, 4]; y = [2, 4, 6, 8]; plt.scatter(x, y)

C. x = [1, 2, 3, 4]; y = [4, 4, 4, 4]; plt.scatter(x, y)

D. x = [1, 2, 3, 4]; y = [1, 3, 2, 4]; plt.scatter(x, y)

Solution

1. Step 1: Identify negative relationship in data

   In x = [1, 2, 3, 4]; y = [10, 8, 6, 4]; plt.scatter(x, y), as x increases, y decreases, showing a negative relationship.

2. Step 2: Check other options for relationship type

   x = [1, 2, 3, 4]; y = [2, 4, 6, 8]; plt.scatter(x, y) shows positive relationship, C shows no change, D shows no clear pattern.

3. Final Answer:

   x = [1, 2, 3, 4]; y = [10, 8, 6, 4]; plt.scatter(x, y) -> Option A

4. Quick Check:

   y decreases as x increases = A [OK]

Hint: Negative relationship means y goes down as x goes up [OK]

Common Mistakes:

• Confusing positive and negative trends
• Choosing data with no clear pattern
• Ignoring constant y values