Scatter plots in MATLAB

Introduction

Scatter plots help you see how two sets of numbers relate to each other. They show points on a graph so you can spot patterns or trends.

To check if there is a relationship between hours studied and exam scores.

To see how temperature changes with time during a day.

To compare sales numbers of two products over several months.

To find out if taller people tend to weigh more.

To explore if advertising budget affects the number of customers.

Syntax

MATLAB

scatter(x, y)
scatter(x, y, size)
scatter(x, y, size, color)
scatter(x, y, size, color, 'filled')

x and y are vectors of the same length representing points.

You can change the size and color of points to add more information.

Examples

Basic scatter plot with points at (x, y).

MATLAB

x = [1 2 3 4 5];
y = [2 4 1 3 5];
scatter(x, y)

Scatter plot with larger points (size 100).

MATLAB

x = rand(1,10);
y = rand(1,10);
scatter(x, y, 100)

Scatter plot with colored and filled points.

MATLAB

x = 1:5;
y = [5 3 6 2 7];
colors = [10 20 30 40 50];
scatter(x, y, 100, colors, 'filled')

Sample Program

This program plots prime numbers (y) against their position (x). Points are red and filled for clear visibility.

MATLAB

x = [1 2 3 4 5 6 7 8 9 10];
y = [2 3 5 7 11 13 17 19 23 29];
scatter(x, y, 100, 'r', 'filled')
title('Scatter plot of x vs y')
xlabel('x values')
ylabel('y values')

Important Notes

Use hold on to add multiple scatter plots on the same figure.

Use colorbar to show what colors mean if you use color to represent data.

Always label your axes and add a title for clarity.

Summary

Scatter plots show points to explore relationships between two variables.

You can customize point size and color to add more meaning.

Label your plot to make it easy to understand.

Practice

1. What does a scatter plot in MATLAB primarily show?

easy

A. A bar chart of grouped data

B. A continuous line connecting data points

C. Points representing pairs of values on an X-Y graph

D. A pie chart of category percentages

Solution

1. Step 1: Understand scatter plot purpose

   A scatter plot shows individual points for pairs of values, usually X and Y coordinates.

2. Step 2: Compare options to definition

   Only Points representing pairs of values on an X-Y graph describes points on an X-Y graph, which matches scatter plot behavior.

3. Final Answer:

   Points representing pairs of values on an X-Y graph -> Option C

4. Quick Check:

   Scatter plot = points on X-Y graph [OK]

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

Common Mistakes:

• Confusing scatter plot with line plot
• Thinking scatter plots show bars or pie slices
• Assuming scatter plots connect points

2. Which of the following is the correct MATLAB syntax to create a scatter plot of vectors x and y?

easy

A. plot.scatter(x, y)

B. scatter(x, y)

C. scatterplot(x, y)

D. scatter x, y

Solution

1. Step 1: Recall MATLAB scatter syntax

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

2. Step 2: Check other options for syntax errors

   Options A, C, and D are not valid MATLAB commands for scatter plots.

3. Final Answer:

   scatter(x, y) -> Option B

4. Quick Check:

   scatter function syntax = scatter(x, y) [OK]

Hint: Use scatter() function with parentheses and commas [OK]

Common Mistakes:

• Using dot notation like plot.scatter
• Typing scatterplot instead of scatter
• Omitting parentheses or commas

3. What will the following MATLAB code display?

x = 1:5;
y = [2 4 6 8 10];
scatter(x, y, 100, 'r', 'filled')

medium

A. A scatter plot with red filled circles sized 100 at points (1,2), (2,4), ..., (5,10)

B. A line plot connecting points from (1,2) to (5,10)

C. An error because 'filled' is not a valid option

D. A scatter plot with default size and blue color points

Solution

1. Step 1: Understand scatter parameters

   The code uses scatter(x, y, 100, 'r', 'filled') which sets point size to 100, color red ('r'), and fills the markers.

2. Step 2: Interpret the plot output

   The plot shows red filled circles at points (1,2), (2,4), (3,6), (4,8), and (5,10).

3. Final Answer:

   A scatter plot with red filled circles sized 100 at points (1,2), (2,4), ..., (5,10) -> Option A

4. Quick Check:

   scatter(x,y,100,'r','filled') = red filled circles [OK]

Hint: Size, color, and fill control marker appearance [OK]

Common Mistakes:

• Thinking 'filled' causes error
• Confusing scatter with line plot
• Ignoring size and color parameters

4. Identify the error in this MATLAB code for a scatter plot:

x = 1:4;
y = [5 6 7];
scatter(x, y)

medium

A. Vectors x and y have different lengths causing an error

B. scatter requires a third argument for size

C. scatter cannot plot numeric vectors

D. No error; code runs fine

Solution

1. Step 1: Check vector lengths

   Vector x has length 4, but y has length 3, which is invalid for scatter.

2. Step 2: Understand scatter input requirements

   Scatter requires x and y to be the same length to plot pairs of points.

3. Final Answer:

   Vectors x and y have different lengths causing an error -> Option A

4. Quick Check:

   Length mismatch in x,y vectors = error [OK]

Hint: x and y must be same length for scatter [OK]

Common Mistakes:

• Assuming scatter auto-fixes length mismatch
• Thinking size argument is mandatory
• Believing scatter can't plot numeric data

5. You have two groups of data points:

x1 = [1 2 3]; y1 = [4 5 6];
x2 = [1 2 3]; y2 = [7 8 9];

How can you plot both groups on the same scatter plot with different colors using filled markers and add a legend?

hard

A. plot(x1, y1, 'b'); plot(x2, y2, 'r'); legend('Group 1', 'Group 2')

B. scatter(x1, y1, 'b', 'filled'); scatter(x2, y2, 'r', 'filled'); legend('Group 1', 'Group 2')

C. scatter(x1, y1, 'b'); hold on; scatter(x2, y2, 'r'); legend('Group 1', 'Group 2')

D. scatter(x1, y1, 'b', 'filled'); hold on; scatter(x2, y2, 'r', 'filled'); legend('Group 1', 'Group 2')

Solution

1. Step 1: Plot first group with filled blue markers

   Use scatter(x1, y1, 'b', 'filled') to plot blue filled points.

2. Step 2: Use hold on before plotting second group

   To overlay plots, hold on keeps the first plot visible before adding the second.

3. Step 3: Plot second group with filled red markers and add legend

   Plot second group with scatter(x2, y2, 'r', 'filled') and add legend for clarity.

4. Final Answer:

   scatter(x1, y1, 'b', 'filled'); hold on; scatter(x2, y2, 'r', 'filled'); legend('Group 1', 'Group 2') -> Option D

5. Quick Check:

   Use hold on to overlay scatter plots with legend [OK]

Hint: Use hold on to combine scatter plots with different colors [OK]

Common Mistakes:

• Forgetting hold on causes second plot to overwrite first
• Using plot instead of scatter for points
• Omitting legend or using incorrect syntax