Chapter 5: Statistics: Describing Data
Learning Outcomes
- Create a frequency table, bar graph, pareto chart, pictogram, or a pie chart to represent a data set
- Identify features of ineffective representations of data
- Create a histogram, pie chart, or frequency polygon that represents numerical data
- Create a graph that compares two quantities
In this lesson we will present some of the most common ways data is represented graphically. W e will also discuss some of the ways you can increase the accuracy and effectiveness of graphs of data that you create.
Presenting Categorical Data Graphically
Visualizing Data
Categorical, or qualitative, data are pieces of information that allow us to classify the objects under investigation into various categories. We usually begin working with categorical data by summarizing the data into a frequency table.
Frequency Table
A frequency table is a table with two columns. One column lists the categories, and another for the frequencies with which the items in the categories occur (how many items fit into each category).
Example
An insurance company determines vehicle insurance premiums based on known risk factors. If a person is considered a higher risk, their premiums will be higher. One potential factor is the color of your car. The insurance company believes that people with some color cars are more likely to get in accidents. To research this, they examine police reports for recent total-loss collisions. The data is summarized in the frequency table below.
| Color | Frequency |
| Blue | 25 |
| Green | 52 |
| Red | 41 |
| White | 36 |
| Black | 39 |
| Grey | 23 |
Sometimes we need an even more intuitive way of displaying data. This is where charts and graphs come in. There are many, many ways of displaying data graphically, but we will concentrate on one very useful type of graph called a bar graph. In this section we will work with bar graphs that display categorical data; the next section will be devoted to bar graphs that display quantitative data.
Bar graph
A bar graph is a graph that displays a bar for each category with the length of each bar indicating the frequency of that category.
To construct a bar graph, we need to draw a vertical axis and a horizontal axis. The vertical direction will have a scale and measure the frequency of each category; the horizontal axis has no scale in this instance. The construction of a bar chart is most easily described by use of an example.
example
Using our car data from above, note the highest frequency is 52, so our vertical axis needs to go from 0 to 52, but we might as well use 0 to 55, so that we can put a hash mark every 5 units:
Notice that the height of each bar is determined by the frequency of the corresponding color. The horizontal gridlines are a nice touch, but not necessary. In practice, you will find it useful to draw bar graphs using graph paper, so the gridlines will already be in place, or using technology. Instead of gridlines, we might also list