Chapter 8 Statistics
8.2 Visualizing Data
Learning Objectives
By the end of this section, you will be able to:
- Create charts and graphs to appropriately represent data
- Interpret visual representations of data
- Determine misleading components in data displayed visually
Summarizing raw data is the first step we must take when we want to communicate the results of a study or experiment to a broad audience. However, even organized data can be difficult to read; for example, if a frequency table is large, it can be tough to compare the first row to the last row. As the old saying goes, a picture is worth a thousand words (or, in this case, summary statistics)! Just as our techniques for organizing data depended on the type of data we were looking at, the methods we’ll use for creating visualizations will vary. Let’s start by considering categorical data.
Visualizing Categorical Data
If the data we’re visualizing are categorical, then we want a quick way to represent graphically the relative numbers of units that fall in each category. When we created the frequency distributions in the last section, all we did was count the number of units in each category and record that number (this was the frequency of that category). Frequencies are nice when we’re organizing and summarizing data; they’re easy to compute, and they’re always whole numbers. But they can be difficult to understand for an outsider who’s being introduced to your data.
Let’s consider a quick example. Suppose you surveyed some people and asked for their favorite color. You communicated your results using a frequency distribution. Jerry is interested in data on favorite colors, so he reads your frequency distribution. The first row shows that 12 people indicated green was their favorite color. However, Jerry has no way of knowing if that’s a lot of people without knowing how many people total took your survey. Twelve is a pretty significant number if only 25 people took the survey, but it’s next to nothing if you recorded 1,000 responses. For that reason, we will often summarize categorical data not with frequencies but with proportions. The proportion of data that fall into a particular category is computed by dividing the frequency for that category by the total number of units in the data.
[latex]\text{Proportion of a category} = \frac{\text{Category frequency}}{\text{Total number of data units}}[/latex]
Proportions can be expressed as fractions, decimals, or percentages.
Example 1
Recall Example 2 in Section 8.1, in which a teacher recorded the responses on the first question of a multiple-choice quiz, with five possible responses (A, B, C, D, and E). The raw data were as follows:
| A | A | C | A | B | B | A |
| E | A | C | A | A | A | C |
| E | A | B | A | A | C | A |
| B | E | E | A | A | C | C |
We computed a frequency distribution that looked like this:
[latex]\begin{array} {|c|c|} \hline \textbf{Response to First Question} & \textbf{Frequency} \\ \hline \text{A} & \text{14} \