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.
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).
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:
- 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)
Whereas scatter plots are used to show change, bar graphs are often used to indicate an amount or level of occurrence of a phenomenon for different categories. Consider the following bar graph. It illustrates the number of employees who were absent due to illness during a particular week in two different age groups.
In this bar graph, the categories are the days of the week, and the frequency represents the number of employees who are sick. It can be immediately seen that younger employees are sick before and after the weekend. There is also an inconsistent trend for the younger employees with data ranging all over the place. During mid-week the older crowd tends to stay home more often.
How many people on average are sick in the 41–65 age group? To find the average, you first must find out how many illnesses occur each week in the particular age group. There are 41 illnesses in total for a five-day period (3 + 10 + 12 + 12 + 4 = 41). To calculate the average, just divide the total illnesses by the number of days for a total of 8.2 illnesses or, more realistically, 8 absences per day.
Pictographs are very similar to bar graphs, but instead of bars indicating frequency, small icons are assigned a key value indicating frequency.
In this pictograph, the key indicates that every icon represents 10 people, so it is easy to determine that there were 12 × 10 = 120 freshmen, 5.5 × 10 = 55 sophomores, 5 × 10 = 50 juniors, and 3 × 10 = 30 seniors.
Pie Charts and Circle Graphs
Pie charts and circle graphs are often used to show what percent of a total is taken up by different components of that whole. This type of graph is representative of a whole and is usually divided into percentages. Each section of the chart represents a portion of the whole, and all of these sections added together will equal 100% of the whole. The following chart shows the three styles of model homes in a new development and what percentage of each there is.
The chart shows the different models of homes. The categories add up to 100% (25 + 30 + 45 = 100). To find the percentage of Estate homes, you can look at the pie chart and see that 45% of the homes are done in the Estate model.
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