Lesson 4: Choosing a Data Display

Property

A bar graph is used specifically for categorical data. It uses rectangular bars separated by gaps to represent the frequency of each category.
A valid bar graph requires a title, labeled axes, and a properly scaled vertical axis. Crucially, the vertical axis (y-axis) showing the frequency MUST start at 0. Starting the axis at a number greater than 0 visually distorts the proportions of the bars.

Examples

• Standard Bar Graph: A horizontal bar graph displaying favorite colors: Red (12 students), Blue (18 students), Green (8 students). The longer the bar, the more popular the choice. The categories are separated by gaps.
• The Zero-Axis Distortion: A graph shows votes for two candidates: Candidate A (52 votes) and Candidate B (48 votes). The true difference is very small. If the vertical axis starts at 40 instead of 0, Candidate A's bar will be 12 units tall and Candidate B's bar will be 8 units tall. This visually makes Candidate A look 50% more popular, misleading the reader.

Explanation

Bar charts are fantastic for comparing discrete groups, which is why there are visible gaps between the bars—the gaps signal that the categories don't bleed into one another. However, you must be a critical reader of graphs! The human eye naturally compares the total height of the bars. If a graph cuts off the bottom by starting the y-axis at a number like 50 instead of 0, it artificially stretches small differences to look like massive gaps.

Property

Graphs are especially useful for illustrating the relationship between two variables. We could instead place a dot at the top of each bar. If we connect the dots with line segments, we have created a line graph. We often use line graphs to illustrate trends in data over time.

Examples

• A line graph shows a student's test scores over a semester: 85 in September, 88 in October, 92 in November, and 90 in December. The line connecting these points shows a general improvement.

• A line graph tracks the daily temperature for a week. The points might be $15^\circ C$, $17^\circ C$, $16^\circ C$, $19^\circ C$, $20^\circ C$, $18^\circ C$, and $17^\circ C$. The line shows the temperature fluctuations.