Data Visualization

Why Visualize Data?

A picture is worth a thousand numbers. Data visualization:

• Reveals patterns not obvious in tables
• Identifies outliers and unusual observations
• Shows distributions at a glance
• Communicates findings effectively to any audience
• Guides analysis by suggesting what methods to use

Choosing the Right Chart

The best visualization depends on your data type and what you want to show:

Charts for Categorical Data

Bar Charts

Bar charts display frequencies or percentages for categorical data using rectangular bars.

Best practices:

• Start the y-axis at zero (avoid misleading comparisons)
• Order bars logically (alphabetical, by size, or natural order)
• Use horizontal bars for long category names
• Limit to 5-7 categories for clarity

Pie Charts

Pie charts show proportions as slices of a circle.

Rules for pie charts:

• Categories must sum to 100%
• Use only for few categories (≤5)
• Order slices by size (largest first, clockwise)
• Avoid 3D effects (distorts perception)

Charts for Numerical Data

Histograms

Histograms show the distribution of numerical data by grouping values into bins.

Reading Histogram Shapes

Box Plots (Box-and-Whisker)

Box plots display the five-number summary visually.

Min    Q1     Median    Q3     Max
 |-----|========|========|-----|
45    65       78       88    98
      |________IQR________|
            = 88-65 = 23

Identifying Outliers with Box Plots

Outliers are points beyond the “fences”:

$\text{Lower fence} = Q_1 - 1.5 \times IQR$ $\text{Upper fence} = Q_3 + 1.5 \times IQR$

Box Plot vs Histogram

Stem-and-Leaf Plots

A hybrid between a table and histogram—shows shape while preserving actual values.

Stem | Leaf
-----|------
  2  | 3 5 8
  3  | 1 2 5 5 8
  4  | 1 2 7

Dot Plots

Simple visualization showing each data point as a dot.

7:  •
8:  • • •
9:  • •
10: • • • •

Charts for Relationships

Scatter Plots

Scatter plots show the relationship between two numerical variables.

Describing Scatter Plot Patterns

Line Charts

Line charts show how a numerical variable changes over time.

Best practices:

• Time always goes on the x-axis
• Don’t connect unrelated points
• Use markers to show actual data points
• Be careful with multiple lines (limit to 4-5)

Comparing Distributions

Side-by-Side Box Plots

Class A: |-----|=====|=====|-----|
Class B:   |---|===|========|------|
Class C: |---|========|======|---|
         40   50   60   70   80   90

Back-to-Back Stem-and-Leaf

Female | Stem | Male
-------|------|--------
 8 6 4 |  5   |
 9 7 5 |  6   | 2 4 6 8
 8 4 2 |  6   | 5 7 9
       |  7   | 0 2 4

Common Visualization Mistakes

1. Truncated Axes

Starting a bar chart y-axis at a non-zero value exaggerates differences.

2. 3D Effects

3D adds nothing but distortion. Stick to 2D.

3. Chartjunk

Excessive decoration (pictures, shading, unnecessary gridlines) distracts from data.

4. Wrong Chart Type

• Pie chart for more than 6 categories
• Line chart for categorical data
• Bar chart for continuous data

5. Missing Labels

Always include:

• Title
• Axis labels with units
• Legend (if multiple series)
• Data source

Choosing the Right Visualization: A Decision Tree

What do you want to show?
├── Distribution of ONE variable
│   ├── Categorical → Bar chart
│   └── Numerical → Histogram or Box plot
├── Relationship between TWO variables
│   ├── Both numerical → Scatter plot
│   ├── Both categorical → Grouped bar chart
│   └── One categorical, one numerical → Box plots by group
├── Change over TIME
│   └── Line chart
└── Part-to-whole COMPOSITION
    └── Pie chart or Stacked bar (if few categories)

Summary

In this lesson, you learned:

• Bar charts for categorical data frequencies
• Pie charts for part-to-whole (use sparingly)
• Histograms show numerical data distribution
• Box plots display five-number summary and outliers
• Scatter plots reveal relationships between two numerical variables
• Line charts show trends over time
• Data type determines appropriate visualization
• Avoid misleading charts (truncated axes, 3D effects, chartjunk)

Practice Problems

1. You have data on customer satisfaction ratings (1-5 stars). What chart would you use?

2. You want to compare the distribution of salaries between three departments. What chart would you use?

3. You have monthly revenue data for the past two years. What chart would you use?

4. Given this histogram shape description: “Most data clustered on the right with a long tail stretching to the left.” Is this left-skewed or right-skewed?

Next Steps

Now that you can visualize data:

• Percentiles and Quartiles - Understand box plot components
• Correlation Analysis - Quantify scatter plot relationships
• Histogram Generator Tool - Create histograms for your data