Data Analysis for Praxis I: Pre-Professional Skills Test Study Guide (page 2)

Data analysis simply means reading graphs, tables, and other graphical forms. You should be able to do the following:

• read and understand scatter plots, graphs, tables, diagrams, charts, figures, and so on
• interpret scatter plots, graphs, tables, diagrams, charts, figures, and so on
• compare and interpret information presented in scatter plots, graphs, tables, diagrams, charts, figures, and so on
• draw conclusions about the information provided
• make predictions about the data

It is important to read tables, charts, and graphs very carefully. Read all of the information presented, paying special attention to headings and units of measure. This section will cover tables and graphs. The most common types of graphs are scatter plots, bar graphs, and pie graphs. What follows is an explanation of each, with examples for practice.

Tables

All tables are composed of rows (horizontal) and columns (vertical). Entries in a single row of a table usually have something in common, and so do entries in a single column. Look at the table below that shows how many cars, both new and used, were sold during the particular months.

Tables are very concise ways to convey important information without wasting time and space. Just imagine how many lines of text would be needed to convey the same information. With the table, however, it is easy to refer to a given month and quickly know how many total cars were sold. It would also be easy to compare month to month. In fact, practice by comparing the total sales of July with October.

In order to do this, first find out how many cars were sold in each month. There were 235 cars sold in July (155 + 80 = 235) and 405 cars sold in October (265 + 140 = 405). With a little bit of quick arithmetic it can quickly be determined that 170 more cars were sold during October (405 – 235 = 170).

Scatter Plots

Whenever a variable depends continuously on another variable, this dependence can be visually represented in a scatter plot. A scatter plot consists of the horizontal (x) axis, the vertical (y) axis, and collected data points for variable y, measured at variable x. The variable points are often connected with a line or a curve. A graph often contains a legend, especially if there is more than one data set or more than one variable. A legend is a key for interpreting the graph. Much like a legend on a map lists the symbols used to label an interstate highway, a railroad line, or a city, a legend for a graph lists the symbols used to label a particular data set. Look at the sample graph below. The essential elements of the graph—the x-axis and y-axis—are labeled. The legend to the right of the graph shows that diamonds are used to represent the variable points in data set 1, while squares are used to represent the variable points in data set 2. If only one data set exists, the use of a legend is not essential.

(Note: This data was used in the preceding example for tables.)

The x-axis represents the months after new management and promotions were introduced at an automobile dealership. The y-axis represents the number of cars sold in the particular month after the changes were made. The diamonds reflect the new cars sold, and the squares show the number of used cars sold. What conclusions can be drawn about the sales? Note that the new and used car sales are both increasing each month at a pretty steady rate. The graph also shows that new cars increase at a higher rate and that there are many more new cars sold per month.

Try to look for scatter plots with different trends:

• increase
• decrease
• rapid increase, followed by leveling off
• slow increase, followed by rapid increase
• rise to a maximum, followed by a decrease
• rapid decrease, followed by leveling off
• slow decrease, followed by rapid decrease
• decrease to a minimum, followed by a rise
• predictable fluctuation (periodic change)
• random fluctuation (irregular change)

Broken Line Graphs

Broken line graphs illustrate a measurable change over time. If a line is slanted up, it represents an increase, whereas a line sloping down represents a decrease. A flat line indicates no change.

In the broken line graph below, the number of delinquent payments is charted for the first quarter of the year. Each week the number of outstanding bills is summed and recorded.

There is an increase in delinquency for the first two weeks and then the level is maintained for an additional two weeks. There is a steep decrease after week 5 (initially) until the ninth week, where it levels off again but this time at 0. The 11th week shows a radical increase followed by a little jump up at week 12, and then a decrease to week 13. It is also interesting to see that the first and last weeks have identical values.

This diagram shows a sequence of events to construct two new objects out of one pipe and a few other parts. First, the instructions show that the pipe must be cut into two pieces with a saw. The next two levels show how the assembly will take place, first adding the end pieces and then bolting in those pieces.

Diagrams could be used to show a sequence of events, a process, an idea, or the relationship between different events or people.

When you see a diagram, first ask what the purpose of it is. What is it trying to illustrate? Then look at the different labeled parts of the diagram. What is the function of each part? How are they interrelated? Take a look at the following diagram:

This diagram is a typical chart of how to start a new project. It starts (on the left), by learning about the assignment from the manager and then investigating several aspects of heading a project, including the client, resources, and budget. Once an overall picture is achieved you will then know how many people will be required for the project in order to create an accurate schedule for the project. There are also reminders and further protocols within the diagram in the links.

Now, take the skills you have learned or honed in this review and apply them to the next practice test.