Lesson 2: Constructing Line Graphs and Bar Graphs

Transcription

1 Lesson 2: Constructing Line Graphs and Bar Graphs Selected Content Standards Benchmarks Assessed: D.1 Designing and conducting statistical experiments that involve the collection, representation, and analysis of data in various forms. D.7 Making inferences from data that are organized in charts, tables, and graphs. Lesson Focus This lesson continues instruction on how to construct the various types of graphs. In this lesson students learn to construct line graphs and bar graphs from tables. They will be expected to analyze various types of graphs given to them in a contextual form GEE 21 Connection Students will be required to: Organize data in a frequency table Construct, label, and scale line graphs and bar graphs. Interpret and summarize a set of experimental data presented in a table, line graph, or bar graph in context. Draw conclusions from a variety of graphs, charts, and tables. Translating Content Standards into Instruction This lesson will teach a student how to choose the best display for data and how to set up a graph that displays the data clearly. Two types of graphs will be covered in this lesson the line graph and the bar graph. In addition we will look at frequency tables. This is another method of organizing data. They can be used to draw frequency polygons, a type of line graph. In order for the students to understand each type of display, the lesson should be activity based. Clear and concise instructions for constructing each graph will be available, and students should have a chance to construct their own. Once students have learned each construction they should be presented with some different types of data and asked how that data could best be displayed. Students should be given a chance to see data displayed in a table and on the resulting graph. The teacher should talk about the various aspects of the graph used. Students should also get a chance to generate a graph of the their own. A. Frequency Tables and Line Graphs Line graphs are sometimes called broken-line graphs. A line graph usually displays data that are measured rather than counted. A graph of this sort uses line segments to show changes and relationships between quantities. A small amount of data can be graphed individually. A large amount of data can be organized in a frequency table and then shown in a line graph called a frequency polygon. Both are shown below. GEE 21 Mathematics Remediation Guide 14 - Data Analysis, Probability and Discrete Math

2 This is an example of a table with a small amount of data and its accompanying graph. The table below gives the lows over a seven-day period in South Louisiana as a cold front moved through the state. (This is also available on a Teacher Master for lesson #2.) Day Temperature (Degrees Fahrenheit) October o October o October o October o October o October o October o How to Construct a Line Graph 1. On a sheet of graph paper draw a horizontal and vertical axis. 2. Make a decision as to what to put on the horizontal and vertical axis. The measurement data is usually put on the vertical axis. Time usually goes on the horizontal axis. 3. Decide how you will scale and label each axis. a. The scales will probably be different on each axis. However, the tic marks should be equally spaced on each axis. Normally each axis begins with zero. However, if the measurement data is large and we want to show the details of that data we need to mark the lower part of the vertical axis with a jagged line to show that numbers lower than the numbers we are interested in are being omitted. For instance, we might be showing dollar value of sales from $50,000 to $100,000. We would draw a jagged piece from the origin with our first number being 50,000. b. Each axis should be labeled so that the viewer knows what information is being represented. 4. Plot each point and then connect the points in order with line segments. 5. Select an appropriate title and write it above the graph. Once you have gone over the information above and shown the students how to draw a line graph, hand out Student Worksheet #1. The price of the gasoline is in dollars and cents. They should understand that the scaling on the vertical axis does not have to be to the nearest penny. They can scale by $.10 or $.20 without loss of accuracy. B. Making a frequency table Statisticians use a frequency table to organize large amounts of data. To make such a table 1. List the classes of data. 2. Tally the data. Each number should fall into a single class. This may be a single number or it may be a range of numbers. 3. Count the tally marks to list the frequency of each class. GEE 21 Mathematics Remediation Guide 15 - Data Analysis, Probability and Discrete Math

3 In the example for this lesson the class will be a single number. Example: Mrs. Johnson took a poll of her class as to their favorite sandwich. Once the choices were tallied, the four favorite sandwiches were listed and students were asked to pick which one they liked the best. The results were as follows: Type of sandwich Tally Number Tuna fish 6 Ham and cheese 11 Toasted cheese 5 Roast Beef 9 Information such as that above is better shown as a bar graph. Instructions for such a graph are given below. Students can learn to construct a frequency table and a bar graph by using the same exercise in the example above. Ask the students to list their favorite sandwich, list the 4 favorites, and then have the students pick their favorite from the four. Count the votes by setting up a frequency table as shown above. After the students have learned to construct a bar graph with the example below, they can construct a bar graph with the four favorite sandwiches above. You could use favorite ice creams, favorite desserts, or favorite snacks in place of sandwiches if you prefer. Student Worksheet #2 has a table that the students should use to build a bar graph using the data provided on total salaries paid by the NBA teams in the midwest division of the Western Conference. C. Bar Graphs Bar graphs display categorical data clearly. Categorical data are data that can be grouped or categorized such as favorite colors, makes of cars, or students favorite pets. A bar graph uses horizontal or vertical bars to compare the number of items in each category. How to Construct a Bar Graph 1. Begin by drawing a vertical and horizontal axis. Select a convenient scale for measuring the numbers in each category. Round large numbers. Use tic marks to indicate points on a scale. This will go on the vertical axis if the bars are vertical and on the horizontal axis if the bars are horizontal. 2. Label the remaining axis with the names of the categories. There will be one bar for each category measured. Each bar should be of the same width and equally spaced. Draw each bar marking each length or height with the number in the category. 3. Label each axis. 4. Select an appropriate title and put it at the top of the page. GEE 21 Mathematics Remediation Guide 16 - Data Analysis, Probability and Discrete Math

4 The table below is on teacher master for lesson #2. Use it to show the students how to construct a bar graph. Stress the importance of correct scaling on the frequency axis. Be sure students understand that the graph is not complete until the vertical and horizontal axes are labeled with the correct information and the graph is given a title. Favorite Student After School Activity Use Computers Activity Earn Money Play Sports Talk on Phone Visit with friends Series Number Sources of Evidence of Student Learning Evidence that the student has a grasp of the material will be through teacher observation of their work as they construct each of the graphs. It is important that they understand how to construct each of these graphs. The open ended problems on the GEE could very well be the type of problem that asks students to organize and display data in one of the required graphs. GEE 21 Connection These benchmarks may be assessed either by multiple-choice questions or a free response question. Below are examples of what students might see in a multiplechoice question. These were taken from the Illinois and Texas state tests either of which can be accessed on the Louisiana Department of Education web site. Activity Number Visit with friends 175 Talk on phone 168 Play sports 120 Earn money 120 Use Computers 65 The students at a local high school were polled concerning their favorite activity. Their choices are listed above. GEE 21 Mathematics Remediation Guide 17 - Data Analysis, Probability and Discrete Math

5 1. During what 10-year period did automobile sales increase the most? Vehicles Sold A B * C D E Year Illinois Standards Achievement Test 2. The emergency room staff at a hospital sees more patients on Friday and Saturday nights than on other nights. The following graph shows the average number of patients seen by the emergency-room staff on each night of the week for the past year. Texas Assessment of Academic Skills Which is the best estimate of the average number of patients seen per night from Sunday through Thursday? A. 60 B. 70 C. 80* D The graph shows the gasoline efficiency of several cars. GEE 21 Mathematics Remediation Guide 18 - Data Analysis, Probability and Discrete Math

6 Which statement is supported by the data? A. Car 1 can travel only half the distance of Car 4 on the same amount of gas. B. The median value for efficiency of all the cars is 30 miles per gallon. C. All the cars meet the federal guideline for fuel efficiency of at least 21 miles per gallon. D. Each car can travel a minimum of 350 miles on a tank of gas. E. The difference in gas mileage between the most efficient car and the least efficient car is more than 15 miles per gallon. Texas Assessment of Academic Skills Attributes of Student Work at the Got-It level For the line graph- Students should be able to work independently with few questions for classmates or teacher The scaling is displayed at equal intervals on both axes. Using graph paper is so helpful. The graph is appropriately named. Both axes are labeled correctly. The data displayed is accurate. For the bar graph- Students should be able to work independently with few questions for classmates or teacher. There is one bar for each category and they are of equal width. Each bar should be appropriately named. The scaling is displayed at equal intervals on both axes. Using graph paper is so helpful. The graph is appropriately named. Both axes are labeled correctly. The data displayed is accurate. Finally, students should be able to look at data and tell which of the two graphs would be appropriate. The bar graphs make comparisons among several items in a given category. The line graphs are used to show the behavior of a variable. Ask the students what graph should be used to display: 1. The number of points scored by the teams in the NBA in the last series of games. (bar) 2. Manuel s weight over a period of years. (line) 3. An automobile s value as the gas mileage increases. (line) 4. Sales of different types of pizzas. (bar) GEE 21 Mathematics Remediation Guide 19 - Data Analysis, Probability and Discrete Math

7 Lesson 2: Constructing Line Graphs and Bar Graphs Teacher Blackline #1 Making a line graph Day October 22 October 23 October 24 October 25 October 26 October 27 October 28 Temperature (Degrees Fahrenheit) 73 o 71 o 71 o 60 o 42 o 35 o 41 o GEE 21 Mathematics Remediation Guide 20 - Data Analysis, Probability and Discrete Math

8 Lesson 2: Constructing Line Graphs and Bar Graphs Teacher Blackline #1 Making a bar graph Activity Number Visit with friends 175 Talk on phone 168 Play sports 120 Earn money 120 Use Computers 65 The students at a local high school were polled concerning their favorite activity. Their choices are listed above. GEE 21 Mathematics Remediation Guide 21 - Data Analysis, Probability and Discrete Math

9 Lesson 2: Constructing Line Graphs and Bar Graphs Student Worksheet #1 The table below shows the average price of gasoline over a twelve year period. Gasoline Prices for Unleaded Regular Year Price 1978 $ $ $ $ $ $ $ $ $ $ $ $ $ Make a line graph of the data. 2. Answer the following questions concerning the data. a) What is the year with the highest annual cost? with the lowest annual cost? b) What is the greatest difference when comparing consecutive years? Why might it be different each month? c) What is the overall pattern? GEE 21 Mathematics Remediation Guide 22 - Data Analysis, Probability and Discrete Math

10 Lesson 2: Constructing Line Graphs and Bar Graphs Student Worksheet #1 Below is a table showing the total salaries paid for each of the NBA teams in the Pacific division in the Western Conference of the NBA. Use this to construct a bar graph showing this information. Sacramento LA Lakers Portland Seattle Phoenix LA Clippers Golden State $46.3 million $58.8 million $86.5 million $50.6 million $53.5 million $29.6 million $41.8 million Will your bars be horizontal or vertical? Vertical bars: Categories go on the horizontal axis Horizontal bars: Categories go on the vertical axis Select a convenient scale for measuring the salaries. Use tic marks to indicate points on the scale. Label the remaining axis with the names of the teams. The will be one bar for each team. Each bar should be of equal width. The bars should be equally spaced. Label each axis. Be sure that an observer knows what the numbers stand for. Select an appropriate title and put it at the top of the page. GEE 21 Mathematics Remediation Guide 23 - Data Analysis, Probability and Discrete Math

11 Lesson 2: Constructing Line Graphs and Bar Graphs Answer Keys The bar graph NBA Teams and Their Salaries Team Salary (millions of dollars) Sacramento LA Lakers Portland Seattle Phoenix LA Clippers Golden State Western Conference Pacific Division Series1 The line graph Price of Gasoline Price $1.60 $1.40 $1.20 $1.00 $0.80 $0.60 $0.40 $0.20 $ Year Beginning in 1978 GEE 21 Mathematics Remediation Guide 24 - Data Analysis, Probability and Discrete Math