Basic Math and Pre-Algebra

PART 4. The State of the World

 

CHAPTER 19. Graphs

 

Information is all around us. Whether in words or in numbers, it comes at us from the news, from the internet, from our studies, and from conversations. Having all the facts is a good thing, but only if you can make sense of all of it. One of the ways to help us make sense of all the information coming at us is to represent it in a well-designed chart or graph. Visual representations of data are often easier to understand than tables full of numbers.

In this chapter, you’ll look at those charts and graphs from both sides. One of the most useful skills you can have is the ability to read a graph and pull the important information from it. Knowing what distinguishes a good graph from a not so good one is important, too. Sometimes the responsibility is on you to produce a graph, and whether you do that by hand or with the help of a computer, you need to know how to do it correctly. This chapter will look at several different types of graphs, how to read them, how to make them, and what kinds of information they best represent.

 

Bar Graph

 

Bar graphs are just what they sound like: graphs that use bars to compare different quantities. The bars are usually vertical, but it is possible to make a horizontal bar graph, too. Each bar represents a different quantity, and the height (or horizontal length) of the bar corresponds to the size of the number.

 

When to Use It

Bar graphs are usually used to compare the sizes of different categories of information. The labels on the horizontal axis are usually the names of the categories, and the heights of the bars show the sizes of each category. The bars may be in size order (in which case the graph is sometimes called a Pareto chart) or in some order that makes sense for the categories.

Bar graphs can also be used to show the change in some value over time, although a line graph is probably a better choice. In that case, the labels on the horizontal axis may be dates, months, years, or other time intervals.

 

How to Draw It

If you wanted to show the relative sizes of the four classes in County High School, you might make a bar graph, with a bar to represent each class. If the freshman class has 583 students, the sophomore class 529, the junior class 492, and the senior class 451, you’d want to draw a horizontal axis with a space of equal size for each of the bars. Usually, you leave a little space between the bars. Then you’ll need a vertical axis with a scale that lets you show the different class sizes. The largest class is 583, so your vertical axis needs to go at least that high, and it needs to be divided into small enough units that you can find 583, 529, 492 and 451. If you try to do a scale from 0 to 600 by tens, you may run into a problem.

 

 

Either the vertical axis will become so crowded with numbers that you can’t read them anymore, or the graph will become so big that it won’t fit on the page. What can you do? One strategy is not to label every division. They’re still there to help you to count the height of the bars, but the scale is easier to read.

 

 

The other tactic you can use is what’s called a broken scale. At the bottom of the vertical axis, you place a pair of slashes or a zigzag marker to show that you’re skipping over some numbers, and then you begin the scale again after the break. This graph has a broken axis that picks up at 300.

 

 

MATH TRAP

When a graph has a broken scale, the relative sizes of the bars can be distorted. If the scale jumps from zero to 500 in a short break, a bar that represents 700 could look almost twice the size of a bar that represents 600. Read carefully. Always check for broken scales and note how much of a jump they've taken.

 

So what does the bar graph for the four classes at County High School look like? You draw a bar for each class, making sure that the bars are all the same width, and bringing each up to a point on the scale that corresponds to the enrollment. You might want to label the bars with the actual values they represent, especially if the scale is hard to read.

 

 

How to Read It

When you begin to read a bar graph, look first at the words around the graph. Is there a title to tell you what the graph is about? Are the scales labeled to tell you what they show and in what units they’re measured? Then look at the actual bars. How high is each bar? You may need to estimate the quantities, if exact values are not given. Be sure to read scales carefully.

 

 

 

This graph shows the best times in speed skating for athletes from different countries in the 2002 Winter Olympics. The horizontal axis shows the names of the countries. The vertical scale shows times in seconds. It’s easy to see that the athletes from Belarus were significantly slower than those of the other countries represented. It’s a little harder to find the fastest country, because several countries have times just over 69 seconds.

 

CHECK POINT

1. Draw a bar graph to represent the data below.

Average Gasoline Usage in Hundreds of Gallons per Month for New England States

State

CT

ME

MA

NH

RI

Gasoline Usage

4.3

5.4

4.4

5.4

4.1

 

2. Which state had the lowest average gasoline usage? Why might residents of that state use less gasoline?

The bar graph below summarizes the sales of various lunches offered in a school cafeteria.

 

 

3. Based upon this information, tacos outsell pasta by approximately how many lunches?

4. Approximately how many chicken lunches are sold per year?

5. Approximately how many burgers are sold per year?