Lesson 4: The Graphing Gourmet

Transcription

1 D ATA AND G RAPHS - 28 Lesson 4: The Graphing Gourmet Learning Objectives In this lesson, you will... create a bar graph and a line graph select a graph to use to represent different types of data Materials rulers graph paper In this lesson you will learn how to create bar graphs and line graphs by hand. You will also continue to read and interpret them. Bar graphs display data sets as bars that run either vertically or horizontally. They may be used to illustrate the change in one category over time or to compare the quantities of two or more categories. ACTIVITY 1 INTERPRETING BAR GRAPHS 1. Figure 11 shows a well-constructed bar graph. List at least four characteristics of the bar graph that makes it engaging, informative, and easy to interpret. Domino's Pizza Total Systemwide Sales Sales ($ billions) Figure 11 Domino s Pizza Total Systemwide Sales Source: 2. Describe the overall trend for Domino s Pizza Total Systemwide Sales.

2 D ATA AND G RAPHS What were the total sales in 2001? Write your answer the way it is given in the bar graph and in dollars. 4. What is the increase in sales from 1999 to 2001? 5. Figure 12 compares calories found in one slice of pizza at several restaurants. List at least four characteristics of the bar graph that makes it engaging, informative, and easy to interpret. Figure 12 Calories in One Slice of Cheese Pizza 6. Which two companies offer a slice of cheese pizza with about the same number of calories? How many calories? 7. About how many more calories are in a Pizza Hut slice of cheese pizza than a Little Caesars slice of cheese pizza? 8. What additional information about the different brands of pizza might you be interested in when interpreting this graph? 9. The calories in a slice of Domino s Pizza is about what percent of the calories in a slice of Pizza Hut pizza?

3 D ATA AND G RAPHS - 30 Constructing bar graphs To construct a bar graph, you will need some tools. Graphing calculators and computers make constructing graphs almost automatic, but you will be constructing one with paper, pencil, and a ruler to better understand them. ACTIVITY 2 CONSTRUCTING BAR GRAPHS In this activity, you will construct a bar graph of Papa John s Pizza total systemwide sales for the 5-year period from 1997 to These data can be found in Table 4. For the year Total systemwide sales ($ millions) Table 4 Papa John s Pizza Total Systemwide Sales Source: 1. When graphing data over a period of time, the time increments are usually placed on the horizontal axis and are evenly spaced (by day, month, year, etc.). The dates should move toward the present from left to right. Explain how you will create the horizontal axis for these data. 2. On Figure 13, on the next page, label the horizontal axis with the years. Make the years about half an inch apart. 3. The other data type (in this case, sales) will be placed along the vertical axis. To determine the values for the vertical axis, you need to determine the range of the data set by calculating the difference between the highest and lowest value. What is the range of this data set? 4. Now, you will choose a convenient increment to move from the lowest to the highest value. Discuss some possibilities and record your ideas here. 5. Choose a convenient increment and determine the number of tick marks on the vertical scale. Do this by dividing the range by the desired increment amount (and round). You may need to change the increment you first chose.

4 D ATA AND G RAPHS Choose a starting value. Starting at zero usually provides a more accurate picture; however, it is not always necessary. If you choose not to start at zero, you need to place a jagged line on the vertical axis to warn readers that you have left out some numbers. It is always necessary to start at a number below the lowest value in the data set. Record your starting value here. 7. On Figure 13, label the vertical axis by starting at your chosen starting point and incrementing by your chosen increment. 8. For each year, draw a bar whose top is at the appropriate level for that year. For example, in 1999 the total sales for Papa John s was $ million. Above 1999, draw a rectangle that stops at about Use a ruler to get a nice graph. 9. Finish your bar graph by giving it a title and labeling the axes with words that describe what is being measured. For example, the horizontal axis could be labeled Year. Figure 13 Papa John s Pizza Total Systemwide Sales

5 D ATA AND G RAPHS - 32 ACTIVITY 3 STACKED BAR GRAPHS In 2002, Yum! Brands had several fast-food restaurants as subsidiaries. Pizza Hut, Taco Bell, Kentucky Fried Chicken, Long John Silver s, and A&W were all part of Yum! Brands. A stacked bar graph can be used to display the sales of the five restaurants combined over time. A stacked bar graph combines data about several different topics in one bar. Each sub-piece of the bar reflects the size of the data it is representing, and the whole bar represents the total. In 2000, the five restaurants had combined sales of $15.5 billion, so the bar is at that height (see Figure 14). Pizza Hut accounts for $5.0 billion, KFC accounts for $4.4 billion, Taco Bell accounts for $5.1 billion, Long John Silver s accounts for $0.7 billion, and A&W accounts for $0.3 billion The bar is divided into these pieces. Each piece has a label or some special marking to differentiate it. With a stacked bar graph, you can see the trend of the sales of the restaurants combined and individually Systemwide Sales Sales ($ billions) A&W Taco Bell KFC Pizza Hut Long John Silver s 0 Yum! Brands Burger King Domino's Dairy Queen Sbarro Restaurants Figure 14 Systemwide Sales for Selected Restaurants Source: 1. If each of the Yum! Brands restaurants were graphed individually, which restaurant of all those listed would have the greatest sales? 2. Write the five Yum! Brands restaurants in order from greatest to least in terms of sales. 3. About how many times greater is Burger King s sales than KFC s sales?

6 D ATA AND G RAPHS Write a sentence that compares the sales of two of the restaurants shown in the graph. Line graphs The last type of graph that you will learn about in this lesson is the line graph. Line graphs are created by connecting known data points with line segments. Line graphs are similar to bar graphs in several ways. In both types of graphs, the actual values are used, and they are generally used to illustrate a trend over time. Line graphs are constructed in much the same way as bar graphs. For many of these graphs, the horizontal axis is used for time and the vertical axis for dollar amounts. An additional feature of line graphs is that you can put several lines on the same graph. This will allow you to make comparisons among two or more sets of data with only one graph. Data that can be ordered or counted can be subdivided into two types, discrete and continuous. A set of discrete data are unconnected; that is, no values exist between data points. A set of continuous data are connected, and values exist between the data points. For example, it makes no sense to ask, What lies between a Whopper and a Cheeseburger Deluxe? On the other hand, it does make sense to ask, What lies between December 2003 and December 2004? Nothing exists between a Whopper and a Cheeseburger Deluxe, but there are 12 months between December 2003 and December It would make no sense to use a line graph to plot data on types of hamburgers, because the data are discrete, unconnected. No estimates or predictions are appropriate between data points or beyond the points. On the other hand, nearly all financial data can be considered continuous data. Creating a line graph of continuous data allows us to estimate values that are not given by the data set. ACTIVITY 4 CONSTRUCTING LINE GRAPHS Construct one line graph comparing systemwide sales declared by several companies. Recall how to construct axes appropriately from our previous work with bar graphs. Be sure to look at all the data in the table as you determine what range of values needs to go on each of the axes. Company McDonald s Burger King Yum! Brands Table 5 Systemwide Sales Data ($ billions) Sources: Plot the sales for McDonald s for each year from 1997 to 2001, one point for each year (use the blank graph provided on the next page). Connect each point with a line segment, and label the line McDonald s. 2. Graph the sales data from the two other companies on the same graph. Be sure to label each line.

7 D ATA AND G RAPHS Label both axes and create a title for your graph. WRAP-UP 1. What kind of graph would you use to represent discrete data? 2. Why might you choose to use a line graph over a bar graph for a particular data set?