Creating Bar Graphs and Pie Charts

8.4 Creating Bar Graphs and Pie Charts 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. Population of the World s Largest Urban Areas (U.N. Dept. for Economic and Social Info.) Tokyo, Japan 27,500,000 Mexico, Mexico 17,500,000 Sao Paulo, Brazil 16,500,000 New York, USA 16,000,000 Bombay, India 15,000,000 Shanghai, China 14,000,000 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 decide 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). 30,000,000 20,000,000 10,000,000 [] 647

648 CHAPTER 8 DATA ANALYSIS AND STATISTICS Now, the height of each bar is determined by using the scale created for the axis. Remembering 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 is 1.75 inches. That would be 1 3 inches. Remember, all we can get from a bar graph is a rough approximation of the 4 actual number. 30,000,000 20,000,000 10,000,000 Tokyo Mexico Sao Paulo New York Bombay Shanghai CHECK YOURSELF 1 The following table represents the 1995 population 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) 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 When a graph represents how some unit is divided, a pie chart is frequently used.

CREATING BAR GRAPHS AND PIE CHARTS SECTION 8.4 649 As you might expect, a pie chart is a circle. Wedges (or sectors) are drawn in the circle to show how much of the whole each part makes up. 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. 30% bus 15% walk 55% car (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. CHECK YOURSELF 2 This pie chart represents the results of a survey that asked students whether they bought lunch, brought it, or skipped lunch altogether. 35% bring lunch 20% skip lunch 45% buy lunch (a) What percentage of the students skipped lunch? (b) What percentage of the students did not buy 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.

650 CHAPTER 8 DATA ANALYSIS AND STATISTICS Example 3 Interpreting a Pie Chart This pie chart shows how Sarah spent her $12,000 college scholarship. 50% tuition books and supplies 35% room and board 1% entertainment 4% clothing (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 0.05 12,000 = 600. Therefore, $600 was spent on clothing and entertainment. CHECK YOURSELF 3 This pie chart shows how Rebecca spends an average 24-h school day. 30% class 25% sleeping 30% studying travel 5% meals (a) How many hours does she spend sleeping each day? (b) How many hours does she spend altogether studying and in class? 270 360 90 180 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 1 1 has 360. That means that of the circle has of 4 4 360, which is 90. With a protractor, we can now create our own pie chart.

CREATING BAR GRAPHS AND PIE CHARTS SECTION 8.4 651 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. 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 (Source: Amer. Auto. Manuf. Assn.) To find the size of the slice for each country, we take the given percent of 360. We will create another table column to represent the degrees needed. 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.) Using a protractor, we start with Japan, and mark a section that is 36. Japan, Again, using the protractor we mark the 18 section for Germany and the 18 section for the other countries. Japan, Germany, 5% All others, 5%

652 CHAPTER 8 DATA ANALYSIS AND STATISTICS 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, Germany, 5% All others, 5% U.S., 80% CHECK YOURSELF 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% CHECK YOURSELF ANSWERS 1. 8,000,000 2. (a) 20%; (b) 55% 7,000,000 3. (a) 6 h; (b) 14.4 h 4. 6,000,000 5,000,000 4,000,000 3,000,000 2,000,000 1,000,000 New York, NY Los Angeles, CA Chicago, IL Houston, TX Philadelphia, PA San Diego, CA 42% 3 or more 0 2% 34% 2 22% 1

Name 8.4 Exercises Section Date 1. The following table represents the top six metropolitan areas where immigrants were admitted to the United States in 1996. 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 ANSWERS Create a bar graph from this information. 2. The following information represents the 1997 population of the six largest counties in the United States. 1. 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 Create a bar graph from this information. The following pie chart shows the budget for a local company. The total budget is $600,000. 2. 3. Find the amount budgeted in each of the following categories. 3. Production 4. Taxes 5. Research 6. Operating expenses 7. Miscellaneous Research 15% Production 45% Operating Expenses 20% Miscellaneous Taxes 4. 5. 6. 7. 8. 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 5% entertainment other clothing 30% food 20% rent 5% utilities 20% transportation 9. 10. 11. 12. 13. 653

ANSWERS 14. The following table represents women on active duty in 1998. Service Number of Women Army 56,800 Navy 45,000 Marines 18,600 Air Force 65,700 Coast Guard 36,000 14. Create a pie chart for the information. 15. The following table represents the number of Nobel Prize laureates during the years 1901 to 1993. Country Number 15. United States 170 United Kingdom 69 Germany 59 France 24 USSR 10 Others 88 Create a pie chart for the information. Answers 1. 150,000 120,000 Number 90,000 60,000 30,000 New York, NY Los Angeles, CA Miami, FL Area Chicago, IL Washington, DC Houston, TX 3. $270,000 5. $90,000 7. $60,000 9. $4800 11. $4800 13. $1200 15. USSR 2.38% France 5.71% Others 20.95% Germany 14.05% U.K. 16.43% U.S. 40.48% 654