Reading Graphs and Charts
Chapter 6: Reading Graphs and Charts
Lining Up Data with Line Graphs
A line graphactually consists of a bunch of connected segments. A line graph connects data that occurs sequentially over a period of time. You use a line graph to show how values are connected when one point affects the next one.
For example, a line graph often is used to show how temperatures change during a day, because the temperature one hour affects the temperature the next hour. Another use for a line graph is to show the depreciation of a piece of machinery or other property. The value of an item one year has a bearing on the item’s value the next year. The following sections explain everything you need to know about line graphs.
Creating a line graph
The axes used when creating a line graph have numbers or values represent- ing different aspects of the data. The two axes usually have different number- ing systems, because the values being compared most likely don’t even have the same units. But the numbering on each axis should be uniform — spaced equally and numbered consecutively.
Inches of rain 2
5 10 15 20 25 30 35 40
4 6 8 10 12 14 16 18 20 22 24
Y i e l d
Figure 6-2:
Comparing rainfall and crop yield.
When constructing a line graph, you start out somewhat like you do with a scatter plot: You draw your axes and then place points or dots to represent the numbers from your data. The difference is that you connect one dot to the next with a line segment. You do so in order to show that they’re con- nected and changing.
Believe it or not, even a new Mercedes depreciates in value over the years.
Table 6-2 shows the first few years of one car’s value. Draw a line graph to illustrate the value.
Table 6-2 Depreciation of a Mercedes
Year Value
0 $56,000
1 $43,120
2 $36,650
3 $33,720
4 $31,360
5 $29,160
6 $27,120
7 $25,200
A line graph is used to display the information in Table 6-2, because one year’s value of the car is tied to the previous year’s value and the next year’s value. The line graph shown in Figure 6-3 shows the number of years since the car’s purchase along the horizontal (x) axis and the value of the car on the vertical (y) axis. The line graph helps you see how dramatically the value of the car drops at first and how the drops in the value taper off as the car gets older.
Indicating gaps in graph values
You want your graphs and charts to do a lot of explaining without words. So you need to label the axes carefully, use a uniform scale on the axes, and plot the values carefully.
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Chapter 6: Reading Graphs and Charts
Some data sets don’t cooperate very well when it comes to setting up axes that are constructed correctly and, at the same time, give good information.
Sometimes, for instance, problems arise when you want the intersection of the axes to be 0 and the numbers to increase as you move to the right and upward. But you don’t want your graph to be, say, 6 inches across and 90 inches high just to accommodate the numbering protocol. Instead, in this case, you should indicate a gap in the numbering with a zigzag on the axis.
For example, if you want to create a line graph of the total city budget from 1993 through 2000, you may have to enter numbers in the billions. Even if you knock off all the zeros and label your axis as being billions, the numbers go from $5,168 billion to $5,758 billion. So you wouldn’t get much detail in the graph from the numbers. On the left-hand side of Figure 6-4, you see a graph of the total budget for 8 years. The scale is kept uniform and the numbers on the axis go from $0 to $6,000 billion. You don’t see much detail or movement from year to year considering the breadth of the range.
An alternative is to put in a break,which looks like a zigzag, to show that values are missing in the numbering system on the axis. By doing so, you’re still able to keep the remaining numbers uniformly distributed to give a better picture of what’s going on. In the right-hand graph in Figure 6-4, you
Years
$5,000
$10,000
$15,000
$20,000
$25,000
$30,000
$35,000
$40,000
$45,000
$50,000 $55,000
1 2 3 4 5 6 7
Figure 6-3:
The depreciation in value of a Mercedes.
see how a break in the axis allows more information to be conveyed by spreading out the upper numbers for more detail. With this break, you see the detail on just how quickly the budget is changing during particular years.
Measuring Frequency with Histograms
A histogram isn’t some cold remedy (though, doesn’t it sure sound like it?).
Histogramis another name for a bar graph. But, as you can probably tell, bar graphis a bit more descriptive; in fact, you probably already have a picture in your mind of what a bar graph is. However, because you’ll often hear these graphs called histograms, I’ll stick with that term throughout this section.
Just know that you may see it referred to either way.
A histogramis a graph of frequencies — it shows how many of each. With a bar’s height, a histogram shows the relative amount of each category. Unlike a line graph, a histogram doesn’t have to have sequential numbers or dates along the horizontal axis. Why? Because the value of one category doesn’t affect the next one.
For instance, you can list the states along the bottom of a histogram to show the area or population of each state. Or you can show the production of some product.
Another nice feature of a histogram is that you can compare two entries of each category — perhaps showing the difference between one year’s produc- tion and the next. However, the vertical axis has to be uniform in labeling so that the amounts or frequencies are represented fairly.
6,000 6,000
5,000 4,000 3,000 2,000 1,000
5,000
Year
G 93 94 95 96 97 98 99 Year
G 93 94 95 96 97 98 99
B i l l i o n s o f d o l l a r s
B i l l i o n s o f d o l l a r s
Figure 6-4:
Using a break in the vertical axis.
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Chapter 6: Reading Graphs and Charts
To create a histogram, you start out with intersecting horizontal and vertical axes. You list your categories to be graphed along the horizontal axis, and you label the units along the vertical axis. Draw a thick line or rectangle above each category to its corresponding height. The rectangles will be par- allel to one another, but they’ll usually be different heights.
Create a histogram showing the number of hurricanes that hit the United States in each decade of the 20th century. The numbers are as follows:
1901–1910, 18 1911–1920, 21 1921–1930, 13 1931–1940, 19 1941–1950, 24 1951–1960, 17 1961–1970, 14 1971–1980, 12 1981–1990, 15 1991–2000, 14
The histogram you create should have the decades listed along the horizon- tal axis and the numbers 0 through 24 or 25 on the vertical axis. The bar rep- resenting each frequency should be shaded in. The bars can be touching, but they don’t have to be. Figure 6-5 shows my version of the histogram. I chose not to have the bars touching, because only ten bars are needed.
A histogram makes comparing the relative number of hurricanes over the 20th century quite easy. With this graph, you can easily pick out when there were twice as many hurricanes during one decade than there were in another.
Try another example: Suppose a flag and decorating company sells five differ- ent types of products: flags, banners, table decorations, flag stands, and com- memorative pins. The manager wants you to create a histogram showing the total sales of each category for two consecutive years. Table 6-3 shows the total sales for each category.
Table 6-3 Total Revenue for a Flag and Decorating Company
Category Year 1 Year 2
Flags $450,000 $540,000
Banners $300,000 $330,000
Table decorations $50,000 $90,000
Flag stands $30,000 $40,000
Commemorative pins $160,000 $290,000
You see that each category had an increase in sales. By creating a histogram with the two years’ sales side by side, you can see how the increases com- pare proportionately in each category. Also, the histogram allows you to better understand where the main emphasis is for the company — where most of the revenue comes from in the different sales. See Figure 6-6 to see a completed histogram for this scenario.
A picture can’t tell you everything. You can see the relative changes and the comparable revenue amounts. But if you want to determine the actual per- cent changes and the proportionate amount that each product contributes to the total revenue, you have to figure the percentages. In Chapter 3, you find all the information you need on percent increases and decreases.
Decade 25
20
15
10
5
1901- 1910
1911- 1920
1921- 1930
1931- 1940
1941- 1950
1951- 1960
1961- 1970
1971- 1980
1981- 1990
1991- 2000 H
u r r i c a n e s Figure 6-5:
A histogram showing the number of hurricanes that hit the U.S. each decade of the 20th century.
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Chapter 6: Reading Graphs and Charts
Taking a Piece of a Pie Chart
A pie chartis a circle divided into wedges where each wedge or piece of the pie is a proportionate amount of the total — based on the actual numerical figures. Pie charts are especially useful for showing budget items — where certain amounts of money are going. To create a pie chart, you divide the circle proportionately and draw in the radii(the edges of the pieces). The fol- lowing sections explain pie charts in more detail.
Dividing the circle with degrees and percents
Think of a circle as being divided into 360 separate little wedges. (A circle’s angles all add up to 360 degrees.) Just one of the 360 little wedges is difficult to see — you may not even notice a drawing of one degree in a picture. Table 6-4 shows you many of the more useful fractional divisions of a circle. (I talk more about degrees in Chapter 7, if you need more information.)
$600,000
$500,000
$400,000
$300,000
$200,000
$100,000
Flags Banners Table
decorations
Flag stands
Commemorative pins S
a l e s
r e v e n u e
Year 1
Year 2 Figure 6-6:
A histogram showing two years’
sales.
Table 6-4 Fractional Portions of a Circle
Number of Degrees Fraction and Percent of a Circle
30 . %
360 30
12 1 .8 3
=
45 . %
360 45
8 1 12 5
= =
60 . %
360 60
6 1 .16 7
=
90 %
360 90
4 1 25
= =
120 . %
360 120
3 1 .33 3
=
135 . %
360 135
8 3 37 5
= =
150 . %
360 150
12 5 .41 7
=
180 %
360 180
2 1 50
= =
To give you an idea of how much of a circle some of the angles account for, Figure 6-7 shows you two circles and some wedges drawn in with their respective fractions. You’ll probably need fractions and degree measures other than those shown in the figure, but these circles show you some repre- sentative wedges that you can use to approximate other sizes.
1 4= 90˚
1
8= 45˚ 1
3= 120˚
1 6= 60˚
1 12= 30˚
5 12= 150˚
1 8= 45˚
1 2= 180˚
Figure 6-7:
Wedges of a circle
and their measure- ments.