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1. Session 6 GRAPHS: BAR, CIRCLE AND LINE

2. Session 6 - Objectives • After studying this unit you should be able to • read and interpret data from given vertical and horizontal bar graphs. • read and interpret data from given circle graphs. • read and interpret data from given broken-line, straight-line, and curved-line graphs. • solve word problems requiring the use of graphs. • solve practical shop application problems requiring use of graphs and tables. • identify given table data in terms of constant or variable rates of change and identify the type of graph that would be produced by plotting the data.

3. Session 6 31–1 Types and Structure of Graphs 644 31–2 Reading Bar Graphs 645 31–5 Circle Graphs 657 31–7 Line Graphs 663 31–8 Reading Line Graphs 664 31–9 Reading Combined-Data Line Graphs 666 UNIT EXERCISE AND PROBLEM REVIEW 679

4. Graphs Used to show or represent statistical or technical data in graphic or picture form. Typically, one or four different types. They include picture graphs, bar graphs, circle graphs, and line graphs.

5. Picture Graphs Also called a pictogram, they are easiest to read but often the hardest to create. *Graph used without permission*

6. Bar Graphs Bar graphs also utilize depth to simulate a 3-D image. *Graph used without permission* Three Dimensioanal Bar Graph

7. Bar Graphs Bar graphs can be vertical Vertical Bar Graph *Graph used with permission*

8. Bar Graphs Bar graphs can be horizontal Horizontal Bar Graph *Graph used with permission*

9. Bar Graphs Also called a bar chart, uses solid lines or heavy bars of a definite length to represent given quantities. *Graph used without permission*

10. Circle Graphs Also called pie charts. They are a combination of a circle and divisions (sectors) of the circle into a given number of parts. Two Dimensional Circle Graph *Graph used without permission*

11. Circle Graphs The parts of the circle can be exploded outward for emphasis or highlighting. Exploded Section Circle Graph *Graph used without permission*

12. Circle Graphs Circle graphs also utilize depth to simulate a 3-D image Three Dimensional Circle Graph *Graph used without permission*

13. Line Graphs Are the most widely used graph. They are easy to make and simple to interpret. *Graph used without permission*

14. Line Graphs Line graphs can be simple two-dimensional types. *Graph used without permission* Two Dimensional Line Graph

15. Line Graphs Line graphs also utilize depth to simulate a 3-D image *Graph used without permission* Three Dimensional Line Graph

16. Combined Charts *Graph used without permission*

17. Bar Graphs – Page 645 Bar Graphs contain two scales: -Horizontal scale is called the x-axis -Vertical scale is called the y-axis -Axes usually located on bottom and left of graph at a point called the origin. Scale values vary and depend on data being graphed

18. Bar Graphs – Page 645 The horizontal and vertical scale values vary and depend on the data that are graphed.

19. Bar Graphs – Page 645 • On a bar graph, the lengths of the bars represent given data • The bars may be horizontal or vertical • To read a bar graph, first determine the value of each space on the scale. Locate the end of each bar and project down (vertically) if the bar is horizontal or project across (horizontally) if the bar is vertical • If the end of a bar is not directly on a line, estimate its value

20. Example – Page 645 The bar graph shown on the next slide shows the monthly production of a manufacturing firm over a five-month period. • How many units are produced each month? • How many units are produced during the entire five-month period? • How many units difference is there between the highest and lowest monthly production?

21. a. How many units are produced each month? Example – Page 645-646 June ≈ July ≈ August ≈ September ≈ October ≈ 40,000 42,000 26,000 35,000 32,000

22. b. How many units are produced during the entire five-month period? Example – Page 645-646 June ≈ July ≈ August ≈ September ≈ October ≈ 40,000 42,000 26,000 35,000 _______ 32,000 175,000

23. c. How many units difference is there between the highest and lowest monthly production? Example – Page 645-646 June ≈ July ≈ August ≈ September ≈ October ≈ 40,000 42,000 26,000 35,000 32,000 42,000 – 26,000 = 16,000

24. This bar graph shows United States employment in major occupational groups for a certain year. Each group is represented by a bar. Each bar is divided into the number of males and the number of females employed within the group. So, each bar represents the total number of workers. Because the variables in each group are stacked, this is often called a stacked bar graph. Example – Page 646-647

25. a. How many men are employed in service occupations? Example – Page 646-647 4.5 million b. How many women are employed in service occupations? 11.5 million c. What percent, to the nearest whole percent, of the clerical group is made up of women? 11,500,000 ÷ 15,000,000 = 0.766 = 77%

26. 2. The bar graph in shows United States production aluminum for each of eight consecutive years. Notice the gap between the two jagged lines near the bottom of the graph. This gap is to show that the production numbers between 0.1 and 1.4 have been eliminated. This is often done to make it easier to read the graph. Exercise 31-2 Page 649

27. b. How many more tons of aluminum were produced during the last year than during the first year of the eight-year period? Exercise 31-2 Page 649 • 1 ≈ • 2 ≈ • 3 ≈ • 4 ≈ • ≈ • ≈ • ≈ • ≈ 1.4 million 1.9 million 2.7 million 3.3 million 3.9 million 4 million 3.9 million 4.1 million 4.1 – 1.4 = 2.7 million

28. c. What is the percent increase in production of the last year over the first year of the eight year period? Exercise 31-2 Page 649 • 1 ≈ • 2 ≈ • 3 ≈ • 4 ≈ • ≈ • ≈ • ≈ • ≈ 1.4 million 1.9 million 2.7 million 3.3 million 3.9 million 4 million 4.1 – 1.4 = 2.7 million 3.9 million 4.1 million 4.1 ÷ 1.4 = 293%

29. Circle Graphs – Page 657 Circle graphs or pie charts show a comparison of parts to each other and to the whole. Circle graphs are often drawn using a protractor because it compares quantities by means of angles constructed from the center of the circle. A complete circle represents the whole amount or 100%. It is divided into sectors. Each sector represents the percent comparing itself to the other parts and to the whole.

30. Example – Page 658-659 How two million dollars is spent in a particular Community. \$560,000 \$240,000 \$200,000 \$300,000 \$700,000 Total \$2,000,000

31. A particular industry employs 10,080 women and 25,200 men. Determine what percentage is women. Example Women

32. A particular industry employs 10,080 women and 25,200 men. Determine what percentage is men. Example Men

33. Example Determine the number of men in the 18-35 year age group

34. Example Determine the number of men in the 36-55 year age group

35. Example Determine the number of women in the 18-35 year age group

36. Example Determine the number of women in the 36-55 year age group

37. 6. The circle graph shows the percent of new vehicle sales in the United States during a given year. If the total sales were 17,118,000 vehicles, use the circle graph to determine the following: Exercise 31-5 Page 660 a. The number of domestic new cars that were sold. 17,118,000 x 34.2% 5,854,356

38. 6. The circle graph shows the percent of new vehicle sales in the United States during a given year. If the total sales were 17,118,000 vehicles, use the circle graph to determine the following: Exercise 31-5 Page 660 b. The total number of imported light trucks that were sold. 17,118,000 x 6.2% 1,061,316

39. Line Graphs – Page 663 Line Graphs contain two scales: -Horizontal scale is called the x-axis -Vertical scale is called the y-axis -Axes usually located on bottom and left of graph at a point called the origin. Scale values vary and depend on data being graphed

40. Line Graphs – Page 663

41. Line Graphs – Page 663 • Show changes and relationships between quantities • Line graphs are used to graph two general types of data: • Data where there is no causal relationship between quantities • Data where there is a causal relationship between quantities

42. Line Graphs – Page 663 • Data where there is not a causal relationship between quantities can be shown with a broken-line graph • The time and temperature graph shows a changing condition usually identified by a broken line. This type of graph is called a broken line graph

43. Line Graphs – Page 663 • When quantities are related to each other by a mathematical rule or formula, the graph is shown as a straight-line graph or curved-line graph • A graph of the perimeters of a square in relation to the lengths of their sides would be shown as a straight-line graph • A graph of the areas of squares in relation to the lengths of their sides would be shown as a curved-line graph

44. Line Graphs – Page 663 • Quantities that are related to each other by a mathematical rule or formula is usually a straight line or a smooth curve • The graph shown is an example of a straight-line graph • The quantities are the perimeters of squares in relation to the lengths of their sides • The formula for perimeter is 4 times the side, P = 4s

45. Line Graphs – Page 663 • This graph is an example of a curved-line graph • The quantities are the areas of squares in relation to the lengths of their sides • The formula for the area of a square is area equals the square of the side, A = s2

46. Line Graphs – Page 664 • Read as follows: • Locate value on one scale • Project value to a point on graphed line • Project from point to other scale • More data can generally be obtained from a line graph than from a bar graph

47. Line Graphs – Page 665 2. The broken-line graph shows the percent of defective pieces of the total production for the next ten consecutive days of production. On what dates were there 6.5% defective pieces? February 13th and 15th

48. Exercise 31-9 – Page 667 2. The surface or rim speed of a wheel is the number of feet that a point on the rim of the wheel travels in one minute. The surface speed depends on the size of the wheel diameter and on the number of revolutions per minute (r/min) that the wheel is turning. The following graph shows the surface speeds of different diameter wheels. All wheels are turning at 320 revolutions per minute. Express the answers for surface speeds to the nearest 10 feet per minute and for diameters to the nearest 0.2 inch.

49. Exercise 31-9 Page 668 a. What is the surface speed of each of the wheel diameters shown on the graph? 80 SFM 160 SFM 250 SFM 330 SFM 420 SFM 500 SFM

50. Exercise 31-9 Page 668 b. What is the surface speed of a 3.6-inch diameter wheel? 300 SFM c. What is the surface speed of a 4.6-inch diameter wheel? 380 SFM