Data Organization and Interpretation for Praxis II ParaPro Test Prep Study Guide (page 4)
The practice quiz for this study guide can be found at:
To answer the data-based questions on the ParaPro Assessment, you will need to understand how to interpret graphs and tables, as well as find the mean, median, and mode of a data set.
Graphs and Tables
On the ParaPro Assessment you will see graphs, tables, and other graphical forms. You should be able to do the following:
- read and understand graphs, tables, diagrams, charts, figures, etc.
- interpret graphs, tables, diagrams, charts, figures, etc.
- compare and contrast information presented in graphs, tables, diagrams, charts, figures, etc.
- 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 pictographs, bar graphs, line 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 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 is also easy to compare month to month. Practice using tables 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 be determined quickly that 170 more cars were sold during October (405 – 235 = 170).
A bar graph is a 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, in two different age groups, who were absent due to illness during a particular week.
In this bar graph, the categories are the days of the week, and the bars indicate the number of employees who are sick, giving overall data on the frequency of sick days among employees. It can be seen immediately that more of the younger employees are sick before and after the weekend. There is also some inconsistency among the younger employees, with data ranging all over the place. During mid-week, the older crowd tends to stay home more often.
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.
Circle graphs are often used to show what percent of a whole is taken up by different components of that whole. This type of graph is representative of a total amount, 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%. 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 styles of model 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 style.
If you know the total number of items in a circle graph, you can calculate how many there are of each component. You just need to multiply the percent by the total.
There are 500 homes in the new development. How many of them are chateaus?
To calculate the number of components (chateaus) out of the total (500), you need to multiply the percent times the total.
25% × 500 = 0.25 × 500 = 125
There are 125 chateaus in the development.
A line graph is a graph used to show a change over time. The line moves from left to right to show how the data changes over a time period. 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 line graph below, the number of delinquent payments is charted for the first quarter of the year. Each week, the number of customers with outstanding bills is added together 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 five (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 at week 13. It is also interesting to see that the first and last weeks have identical values.
This line graph shows an obvious trend because the points go up as the line moves to the right. That means there is a positive trend. A question on the ParaPro Assessment may ask you to make a prediction based on the trend. Each year, the profits of the company go up by about $3 million. Therefore, if you were asked to predict the profits of the company in 2010, you could add $3 million to the profits in 2009. An appropriate prediction for the company's total profits in 2010, based on the trend in the graph, would be $21 million.
Mean, Median, and Mode
It is important to understand trends in data. To do that, look at where the center of the data lies. There are a number of ways to find the center of a set of data.
Average usually refers to the arithmetic mean (usually just called the mean). To find the mean of a set of numbers, add all of the numbers together and divide by the quantity of numbers in the set.
average = (sum of set) ÷ (quantity of set)
Find the average of 9, 4, 7, 6, and 4.
(Divide by 5 because there are five numbers in the set.) The mean, or average, of the set is 6.
Another center of data is the median, which is the number in the center, if you arrange all the data in ascending or descending order. To find the median of a set of numbers, arrange the numbers in ascending or descending order and find the middle value. If the set contains an odd number of elements, then choose the middle value. If the set contains an even number of elements, simply average the two middle values.
Find the median of the number set: 1, 5, 4, 7, 2.
First arrange the set in order—1, 2, 4, 5, 7—and then find the middle value. Because there are five values, the middle value is the third one: 4. The median is 4.
Find the median of the number set: 1, 6, 3, 7, 2, 8.
First arrange the set in order—1, 2, 3, 6, 7, 8—and then find the middle values, 3 and 6.
Find the average of the numbers 3 and 6:
= 4.5. The median is 4.5.
The mode of a set of numbers is the number that appears the greatest number of times.
Find the mode for the following data set: 1, 2, 5, 9, 4, 2, 9, 6, 9, 7.
For the number set 1, 2, 5, 9, 4, 2, 9, 6, 9, 7, the number 9 is the mode, because it appears the most frequently.
The practice quiz for this study guide can be found at:
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