Basic Math and Pre-Algebra For Dummies (82 page)

This area is approximate because I use 3.14 as an approximate value for π. (
Note:
In the preceding problem, I use equals signs when a value is equal to whatever comes right before it, and I use “approximately equal to” signs [≈] when I round.)

Now use this area to find the volume of the cylinder:

Notice how multiplying square inches (in.
²
 ) by inches gives a result in cubic inches (in.
³
 ).

Chapter 17

In This Chapter

Making comparisons with a bar graph

Dividing things up with a pie chart

Charting change over time with a line graph

Plotting points and lines on an
xy
-graph

A
graph
is a visual tool for organizing and presenting information about numbers. Most students find graphs relatively easy because they provide a picture to work with rather than just a bunch of numbers. Their simplicity makes graphs show up in newspapers, magazines, business reports, and anywhere clear visual communication is important.

In this chapter, I introduce you to four common styles of graphs: the bar graph, the pie chart, the line graph, and the
xy
-graph. I show you how to read each of these styles of graphs to obtain information. I also show you how to answer the types of questions people may ask when they want to check your understanding.

In this section, I show you how to read and understand three styles of graphs:

• The bar graph
  is best for representing numbers that are independent of each other.
  
• The pie chart
  allows you to show how a whole is cut up into parts.
  
• The line graph
  gives you a sense of how numbers change over time.
  

A bar graph gives you an easy way to compare numbers or values. For example, Figure 
17-1
shows a bar graph comparing the performance of five trainers at a fitness center.

As you can see from the caption, the graph shows how many new clients each trainer has enrolled this quarter. The advantage of such a graph is that you can see at a glance, for example, that Edna has the most new clients and Iris has the fewest. The bar graph is a good way to represent numbers that are independent of each other. For example, if Iris gets another new client, it doesn't necessarily affect any other trainer's performance.

Reading a bar graph is easy when you get used to it. Here are a few types of questions someone could ask about the bar graph in Figure 
17-1
:

• Individual values:
  How many new clients does Jay have?
  Find the bar representing Jay's clients and notice that he has 23 new clients.
  
• Differences in value:
  How many more clients does Rita have than Dwayne?
  Notice that Rita has 20 new clients and Dwayne has 18, so she has 2 more than he does.
  
• Totals:
  Together, how many clients do the three women have?
  Notice that the three women — Edna, Iris, and Rita — have 25, 16, and 20 new clients, respectively, so they have 61 new clients altogether.
  

A
pie chart,
which looks like a divided circle, shows you how a whole object is cut up into parts. Pie charts are most often used to represent percentages. For example, Figure 
17-2
is a pie chart representing Eileen's monthly expenses.

You can tell at a glance that Eileen's largest expense is rent and that her second largest is her car. Unlike the bar graph, the pie chart shows numbers that are dependent upon each other. For example, if Eileen's rent increases to 30% of her monthly income, she'll have to decrease her spending in at least one other area.

Here are a few typical questions you may be asked about a pie chart:

• Individual percentages:
  What percentage of her monthly expenses does Eileen spend on food?
  Find the slice that represents what Eileen spends on food and notice that she spends 10% of her income there.
  
• Differences in percentages:
  What percentage more does she spend on her car than on entertainment?
  Eileen spends 20% on her car but only 5% on entertainment, so the difference between these percentages is 15%.
  
• How much a percent represents in terms of dollars:
  If Eileen brings home $2,000 per month, how much does she put away in savings each month?
  First notice that Eileen puts 15% every month into savings. So you need to figure out 15% of $2,000. Using your skills from Chapter
  12
  , solve this problem by turning 15% into a decimal and multiplying:
  
  • $2,000 × 0.15 = $300
    

  So Eileen saves $300 every month.
  

The most common use of a
line graph
is to plot how numbers change over time. For example, Figure 
17-3
is a line graph showing last year's sales figures for Tami's Interiors.

The line graph shows a progression in time. At a glance, you can tell that Tami's business tended to rise strongly at the beginning of the year, drop off during the summer, rise again in the fall, and then drop off again in December.

Here are a few typical questions you may be asked to show that you know how to read a line graph:

• High or low points and timing:
  In what month did Tami bring in the most revenue, and how much did she bring in?
  Notice that the highest point on the graph is in November, when Tami's revenue reached $40,000.
  
• Total over a period of time:
  How much did she bring in altogether the last quarter of the year?
  A quarter of a year is three months, so the last quarter is the last three months of the year. Tami brought in $35,000 in October, $40,000 in November, and $30,000 in December, so her total receipts for the last quarter add up to $105,000.
  
• Greatest change:
  In what month did the business show the greatest gain in revenue as compared with the previous month?
  You want to find the line segment on the graph that has the steepest upward slope. This change occurs between April and May, where Tami's revenue increased by $15,000, so her business showed the greatest gain in May.
  

When math folks talk about using a graph, they're usually referring to an
xy
-graph (also called the
Cartesian coordinate system
), shown in Figure 
17-4
. In Chapter
25
, I tell you why I believe this graph is one of the ten most important mathematical inventions of all time. You see a lot of this graph when you study algebra, so getting familiar with it now is a good idea.