Creating Bar Graphs and Pie Charts

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8.4 OBJECTIVES

1. Use a table to create a bar graph

2. Read a pie chart

3. Use a table to create a pie chart

As we have seen, it is frequently easier to read information from a graph than it is from a table. In this section, we will look at two types of graphs that can be created from tables. We have already learned to read a bar graph. In our first example, we will create one.

Example 1

Creating a Bar Graph

The following table represents the 1995 population of the six most populated urban areas in the world. Each population is the population of the city plus the population of all of its suburbs. Create a bar graph from the information in the table.

We will let the vertical axis, the vertical line to the left of the graph, represent population. The six urban areas will be placed along the horizontal axis. To create a graph, we must de-cide on the scale for the vertical axis. The following steps will accomplish that.

1. Pick a number that is slightly larger than the biggest number we are to graph. 30,000,000 is slightly larger than 27,500,000.

2. Decide how long the axis will be. It is best if this length easily divides into the number of step 1. To accomplish this division, we will choose 3 inches. 3. Scale the axis by dividing it

with hashmarks. Label each hashmark with the

appropriate number. In this graph, each inch will represent 10,000,000 people (the 30,000,000 divided by the 3 inches results in 10,000,000 people/inch).

Population of the World’s Largest Urban Areas (U.N. Dept. for Economic and Social Info.)

City 1995 Population

Tokyo, Japan 27,500,000

Mexico City, Mexico 17,500,000

Sao Paulo, Brazil 16,500,000

New York City, USA 16,000,000

Bombay, India 15,000,000 Shanghai, China 14,000,000 30,000,000 20,000,000 1995 Population 10,000,000 [City]

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Now, the height of each bar is determined by using the scale created for the axis. Remem-bering that we have 10,000,000 people/inch, we divide each population by 10,000,000. The result is the height of each bar. The height for Mexico City is 1.75 inches. That would be inches. Remember, all we can get from a bar graph is a rough approximation of the actual number. 30,000,000 20,000,000 1995 Population 10,000,000 City T okyo Shanghai Bombay New Y o rk City Sao Paulo Mexico City 13 4 C H E C K Y O U R S E L F 1

The following table represents the 1995population of the six most populated cities in the United States. Each population is the population within the city limits, which is why the New York population is so different from the previous table. Create a bar graph from the information in the table.

Population of the Largest Cities in the United States (Bureau of the Census, U.S. Dept. of Commerce)

City 1995 Population New York, NY 7,500,000 Los Angeles, CA 3,500,000 Chicago, IL 2,750,000 Houston, TX 2,750,000 Philadelphia, PA 1,500,000 San Diego, CA 1,250,000

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Example 2

Reading a Pie Chart

This pie chart represents the results of a survey that asked students how they get to school most often.

(a) What percentage of the students walk to school? We see that 15% walk to school.

(b) What percentage of the students do not arrive by car?

Because 55% arrive by car, there are 100%55%, or 45%, who do not. 30% 15% 55% bus walk car C H E C K Y O U R S E L F 2

This pie chart represents the results of a survey that asked students whether they bought lunch, brought it, or skipped lunch altogether.

(a) What percentage of the students skipped lunch?

(b) What percentage of the students did not buy lunch? 35% skip lunch 20% 45% buy lunch bring lunch

If we know what the whole pie represents, we can also find out more about what each wedge represents. Example 2 illustrates this point.

As you might expect, a pie chartis a circle. Wedges (or sectors) are drawn in the circle to show how much of the whole each part makes up.

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C H E C K Y O U R S E L F 3

This pie chart shows how Rebecca spends an average 24-h school day.

(a) How many hours does she spend sleeping each day?

(b) How many hours does she spend altogether studying and in class? 30% class 25% sleeping 30% studying 10% travel 5% meals

If we are creating a pie chart, how do we know how much of the circle to use for each piece? To make this decision requires a scale be used for the circle. A standard scale has been established for all circles. As we saw in Chapter 7, each circle has 360°. That means that of the circle has of 360°, which is 90°.

With a protractor, we can now create our own pie chart. 1 4 1 4 360 180 270 90 Example 3

Interpreting a Pie Chart

This pie chart shows how Sarah spent her $12,000 college scholarship.

(a) How much did she spend on tuition? 50% of her $12,000 scholarship, or $6000.

(b) How much did she spend on clothing and entertainment?

Together, 5% of the money was spent on clothing and entertainment, and 0.0512,000 = 600. Therefore, $600 was spent on clothing and entertainment.

35% room and board 10% books and supplies 50% tuition 1% entertainment 4% clothing

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Example 4

Creating a Pie Chart

The following table represents the source of automobiles purchased in the United States in 1997. Create a pie chart that represents the same data.

To find the size of the slice for each country, we take the given percent of 360°. We will cre-ate another table column to represent the degrees needed.

Using a protractor, we start with Japan, and mark a section that is 36°.

Again, using the protractor we mark the 18° section for Germany and the 18° section for the other countries.

Japan, 10% Germ any , 5% All o thers, 5 % Japan, 10%

Source of Automobiles Purchased in 1997

Country of Origin Number % of total Degrees

U.S. 6,500,000 80 288

Japan 800,000 10 36

Germany 400,000 5 18

All Others 400,000 5 18

(Source:Amer. Auto. Manuf. Assn.)

Source of Automobiles Purchased in 1997

Country of Origin Number % of total

U.S. 6,500,000 80

Japan 800,000 10

Germany 400,000 5

All Others 400,000 5

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C H E C K Y O U R S E L F 4

Create a pie chart for the following table, which shows TV ownership for all United States homes.

TV Ownership (Nielsen Media Research)

Number of TVs % of U.S. Homes

0 2% 1 22% 2 34% 3 or more 42% C H E C K Y O U R S E L F A N S W E R S 1. 2. (a)20%; (b)55% 3. (a)6 h; (b)14.4 h 4. 2% 0 22% 1 34% 2 42% 3 or more 1995 Population City 1,000,000 2,000,000 3,000,000 4,000,000 5,000,000 6,000,000 7,000,000 8,000,000 San Diego, CA Philadelphia, PA Houston, TX Chicago, IL Los Angeles, CA New Y ork, NY

There is no need to measure the remainder of the pie. What is left is the 288° section for U.S.-made cars. Note that we saved the large section for last. It is much easier to mark the smaller sections and leave the largest for last.

Japan, 10% Germ any , 5% All othe rs, 5% U.S., 80%

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Exercises

1. The following table represents the top six metropolitan areas where immigrants were admitted to the United States in 1996.

Create a bar graph from this information.

2. The following information represents the 1997 population of the six largest counties in the United States.

Create a bar graph from this information.

The following pie chart shows the budget for a local company. The total budget is $600,000.

Find the amount budgeted in each of the following categories.

3. Production 4. Taxes

5. Research 6. Operating expenses

7. Miscellaneous

The following pie chart shows the distribution of a person’s total yearly income of $24,000.

Find the amount budgeted for each category.

8. Food 9. Rent 10. Utilities 11. Transportation 12. Clothing 13. Entertainment 30% food 10% other 5% entertainment 10% clothing 20% transportation 5% utilities 20% rent Production 45% Miscellaneous 10% Taxes 10% Operating Expenses 20% Research 15% City Population Los Angeles, CA 9,145,219 Cook, IL 5,076,786 Harris, TX 3,158,095 San Diego, CA 2,722,650 Maricopa, AZ 2,696,198 Orange, CA 2,674,091 Area Number New York, NY 133,168 Los Angeles, CA 64,285 Miami, FL 41,527 Chicago, IL 39,989 Washington, DC 34,327 Houston, TX 21,387

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14. The following table represents women on active duty in 1998.

Create a pie chart for the information.

15. The following table represents the number of Nobel Prize laureates during the years 1901 to 1993.

Create a pie chart for the information.

Answers

1. 3. $270,000 5. $90,000 7. $60,000 9. $4800 11. $4800 13. $1200 15. U.S. 40.48% U.K. 16.43% Germany 14.05% France 5.71% USSR 2.38% Others 20.95% 30,000 60,000 90,000 120,000 150,000 Number New Y ork, NY Los Angeles, CA Miami, FL Chicago, IL W ashington, DC Houston, TX Area Country Number United States 170 United Kingdom 69 Germany 59 France 24 USSR 10 Others 88

Service Number of Women