TABE Level D Math: Data Interpretation

In a data interpretation problem you have to draw conclusions from looking at diagram, chart, or table of numbers. You see these in newspapers and magazines all the time.

Unfortunately, there is no set way to interpret one of these figures. You have to read the titles and labels on them carefully in order to understand what is being presented.

The examples below illustrate the various types of figures you will see on the TABE D.

Venn Diagrams

A. Venn diagram is a picture that helps you count objects that may be in two overlapping groups.

Example A. One circle represents a group of men. The other circle represents a group of teachers. The space where the two circles overlap represents people who are both teachers and men. In this picture, there are 12 male teachers, 10 men who aren’t teachers, and 15 teachers who aren’t men. If you were asked how many teachers there are, you would add 12 and 15 and get the answer 27. If you were asked how many men there are, you would add 12 and 10 and get the answer 22.

Graphs

A. graph is a figure that shows how two quantities are related. A graph has a horizontal axis and a vertical axis. Each of the two quantities is measured along one axis.

Example B. The graph below describes a car trip. The horizontal axis measures the amount of time that has passed since the people left home. The vertical axis measures distance traveled. Point A shows a distance of 100 miles in 2 hours. Point B indicates that the travelers stopped for an hour after traveling the first 100 miles (because they had still only traveled 100 miles after 3 hours).


Bar Graphs

A. bar graph is like a graph, except one of the axes represents categories instead of a quantity.
 

Example C. The bar graph below shows the average rainfall for the months. You can tell quickly that March, April, and May are the rainiest months, and that August is the driest month.


Circle Graphs
Circle graphs are good way of showing how a total breaks down into parts. You can think of the circle as a pie and the parts as pieces of pie. The size of each piece corresponds to the percent of the total.

Example D. This circle graph shows the breakdown of favorite summer nonalcoholic drinks. The graph shows that people like soda, water, and iced tea about equally. A smaller percentage of people like fruit drinks.

Favorite Summer Nonalcoholic Beverages

Tables
Tables are another way of showing how two quantities are related. Tables are often used to show how some quantity changes over time.

Example E. The table below shows the population of some town at the end of each year indicated. The population increased gradually between 1950 and 1990. Then it went down between 1990 and 2000.

Annual Population Anytown, U.S.A.

There are two other concepts in data interpretation.

1. Find the mean of a set of numbers.
To find the mean, add the numbers and divide by the number of numbers. This is usually just called the average. For example, the mean of 4, 8, 3, 5, and 10 is 6 (30 ÷ 5)

2. Find the median of a set of numbers.
To find the median, arrange the numbers in order from smallest to largest. There are two cases:
(a) The number of numbers is odd. In this case there is a middle number, and that’s the median.

For example, the median of the five numbers, 4, 8, 13, 25, and 37 is 13.
(b) The number of numbers is even. In this case there are two “middle” numbers. The median is their average.

For example, suppose there are six numbers: 4, 8, 13, 25, 37, and 38. The two middle numbers are 13 and 25.
The median is , the average of 13 and 25.

Data Interpretation Practice

1. The circle graph shows the market share of four major cable TV companies. Which company, if any, has more than half the market share? A. CabCo B. TV4U C. Media Monster D. None

A. radar gun was aimed at 5 cars on the interstate highway. Their speeds were 70 mph, 63 mph, 72 mph, 65 mph, and 60 mph. Use this information to answer questions 2 and 3.

2. What was the median speed? A. 72 mph B. 65 mph C. 66 mph D. 60 mph

3. What was the mean speed? A. 72 mph B. 65 mph C. 66 mph D. 60 mph

Problem: A. jug is being filled with water. The graph shows how much water there is in the jug over time after the filling starts. Use this graph to answer questions 4 and 5.


4. How long did it take to fill the jug with gallon? A. 1 sec B. 2 sec C. 3 sec D. 4 sec

5. How much of the jug was filled after 2.5 seconds? A. 1 gal B. 1.5 gal C. 2 gal D. 2.5 gal

Problem: A. standard die with 6 faces was rolled a hundred times. The outcomes are summarized in the table. Use this table to answer questions 6 and 7.


6. Which face turned up least frequently? A. 1 B. 3 C. 18 D. 24

7. What percent of the time did 6 turn up? A. 6% B. 10% C. 18% D. 24%

8. Middlesex Community College kept track of how many students enrolled in math and English courses. The numbers of students taking math, English, and both types of courses are shown in the Venn diagram. How many students enrolled in math courses? A. 245 B. 200 C. 155 D. 45

Problem: Average high and low temperatures in a certain city were measured in the months of January, April, July, and October. These are shown in the bar graph. Use this graph to do problems 9 and 10.


9. When was the difference between the average high and the average low temperatures the greatest? A. January B. April C. July D. October

10. Which of these is the best estimate of the average high temperature for the 4 months shown in the graph? A. 65°F B. 75°F C. 80°F D. 85°F

Answers: Data Interpretation Practice

1. a

2. b

3. c

4. b

5. c

6. b

7. c

8. a

9. a

10. b