Chapter 7: Organizing and Displaying Data
Introduction
The local arena is trying to attract as many participants as possible to attend the community’s “Skate for Scoliosis” event. Participants pay a fee of $10.00 for registering, and, in addition, the arena will donate $3.00 for each hour a participant skates, up to a maximum of 6 hours. Create a table of values and draw a graph to represent a participant who skates for the entire 6 hours. How much money can a participant raise for the community if he/she skates for the maximum length of time?
This problem will be revisited later in the chapter.
When data is collected from surveys or experiments, it is often displayed in charts, tables, or graphs in order to produce a visual image that is helpful in interpreting the results. From a graph or table, an observer is able to detect any patterns or trends that may exist. The most common graphs that are used in statistics are line graphs, scatter plots, bar graphs, histograms, frequency polygons, circle graphs, and box-and-whisker plots.
- 7.1.
Line Graphs
- 7.2.
Broken-Line Graphs
- 7.3.
Scatter Plots
- 7.4.
Linear Regression Equations
- 7.5.
Pie Charts
- 7.6.
Stem-and-Leaf Plots
- 7.7.
Bar Graphs
- 7.8.
Histograms
- 7.9.
Applications of Histograms
- 7.10.
Frequency Polygons
- 7.11.
Box-and-Whisker Plots
- 7.12.
Applications of Box-and-Whisker Plots
Chapter Summary
Summary
This chapter covers various ways of representing data, and how to use them to calculate certain measures. The types are summarized in the following table:
Graph Type | Description |
---|---|
Line graph | Basic plot in two dimensions, where the points are connected if the variable is continuous. |
Broken-line graph | Graph that connects points by straight lines to show change over time, so the line has no defined slope at the corners. |
Scatter plot | Graph that plots one quantity on the \begin{align*}x\end{align*}-axis and one on the \begin{align*}y\end{align*}-axis to investigate whether or not there is a relationship between the two quantities. |
Pie chart | A circle that is divided into sections (slices) according to the percentage of the frequencies in each class. |
Stem-and-leaf plot | A graph that splits each data point into "stem" and "leaf", putting all leaves with the same stem on the same line. |
Bar graph | A plot made of bars whose heights (vertical bars) or lengths (horizontal bars) represent the frequencies of each category. |
Histogram | A graph in which the classes, or bins, are on the horizontal axis and the frequencies are plotted on the vertical axis. The frequencies are represented by vertical bars that are drawn adjacent to each other. |
Frequency polygon | A graph that uses lines to join the midpoints of the tops of the bars of a histogram or to join the midpoints of the classes. |
Box-and-whisker plot | A graph of a data set in which the five-number summary is plotted. 50 percent of the data values are in the box, and the remaining 50 percent are divided equally on the whiskers. |