1. Unit One Notes: Graphing How do we graph data?

2. Name the different types of graphs (charts).

3. Why do we use graphs?

6. Creating a line graph

7. 1.Draw the Axes: Put the manipulated (independent) variable on the horizontal (x) axis and the (responding) dependent variable on the vertical (y) axis. X Axis – Independent Variable Y Axis – Dependent Variable Remember: Dry Mix What you are collecting data on Changed on purpose M---Manipulated Variable I---Independent Variable X---X- Axis D — Dependent Variable R — Responding Variable Y — Y Axis

8. In class Graphing Practice AB 1 TemperatureHours of heating 2 Stopping distanceSpeed of a car Speed 3 Number of people in a familyCost per week for groceries 4 Amount of rainfallStream flow rate 5 Tree ageAverage tree height 6 Test score Number of hours studying for a test 7 Number of schools neededPopulation of a city Part I: Circle the independent variable in each pair:

9. 2.Label each axis: Label the name of the variable and the measurement units (cm, days, etc.) Ice Cream Sales vs Temperature Temperature °CIce Cream Sales 14.2°$215 16.4°$325 11.9°$185 15.2°$332 18.5°$406 22.1°$522 19.4°$412 25.1°$614 23.4°$544 18.1°$421 22.6°$445 17.2°$408 Temperature (°C) Ice Cream Sales ($)

10. Use this Table to guide you in scaling your graph Range (Highest # - Lowest #) Range ÷ number of boxes Adjusted scale (round # above) Adjusted scale x # boxes Starting value (lowest # or slightly below)- does not have to be zero Ending Value = (Adjusted scale x # boxes)+ starting value

11. Range Temperature: 3.Determine the range: for each variable, take the largest number in the data set and subtract the lowest number. This is the range. Ice Cream Sales vs Temperature Temperature °CIce Cream Sales 14.2°$215 16.4°$325 11.9°$185 15.2°$332 18.5°$406 22.1°$522 19.4°$412 25.1°$614 23.4°$544 18.1°$421 22.6°$445 17.2°$408 25.1 – 11.9 = 13.2

12. Use this Table to guide you in scaling your graph Range (Highest # - Lowest #) Range ÷ number of boxes Adjusted scale (round # above) Adjusted scale x # boxes Starting value (lowest # or slightly below)- does not have to be zero Ending Value = (Adjusted scale x # boxes)+ starting value 13.2

13. 4.Determine the scale: Count the number of squares you have available for each axis. For each axis, take the range and divide by the number of squares. Use even increments. Round up. Temperature (°C) Ice Cream Sales ($) Scale Temperature: 13.2 ÷15 = 0.88

14. Use this Table to guide you in scaling your graph Range (Highest # - Lowest #) Range ÷ number of boxes Adjusted scale (round # above –always up) Adjusted scale x # boxes Starting value (lowest # or slightly below)- does not have to be zero Ending Value = (Adjusted scale x # boxes)+ starting value 13.2 0.88 1 1 x 15 =15

15. 3.Determine the range: for each variable, take the largest number in the data set and subtract the lowest number. This is the range. Ice Cream Sales vs Temperature Temperature °CIce Cream Sales 14.2°$215 16.4°$325 11.9°$185 15.2°$332 18.5°$406 22.1°$522 19.4°$412 25.1°$614 23.4°$544 18.1°$421 22.6°$445 17.2°$408

16. Use this Table to guide you in scaling your graph Range (Highest # - Lowest #) Range ÷ number of boxes Adjusted scale (round # above –always up) Adjusted scale x # boxes Starting value (lowest # or slightly below)- does not have to be zero Ending Value = (Adjusted scale x # boxes)+ starting value 13.2 0.88 1 1 x 15 =15 11 11 + 15 = 26

17. 3.Determine the range: for each variable, take the largest number in the data set and subtract the lowest number. This is the range. Ice Cream Sales vs Temperature Temperature °CIce Cream Sales 14.2°$215 16.4°$325 11.9°$185 15.2°$332 18.5°$406 22.1°$522 19.4°$412 25.1°$614 23.4°$544 18.1°$421 22.6°$445 17.2°$408 If done correctly the ending value should be greater than the highest number in the table

18. Use this Table to guide you in scaling your graph Range (Highest # - Lowest #) Range ÷ number of boxes Adjusted scale (round # above –always up) Adjusted scale x # boxes Starting value (lowest # or slightly below)- does not have to be zero Ending Value = (Adjusted scale x # boxes)+ starting value 13.2 0.88 1 1 x 15 =15 11 11 + 15 = 26

19. Temperature (°C) Ice Cream Sales ($) Add adjusted scale each time 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

20. Part II: Determine the Scale for the following sets of data: ValuesRange # of boxes Range ÷ boxes Adjusted Scale Adjusted scale x # boxes Starting Value Ending Value = (Adjusted scale x # boxes) + starting value 4, 1, 0, 5, 7, 22 15 1.1, 0.95, 1.01, 1.09, 0.98 15 225, 331, 115, 45, 279 20 0.20, 0.04, 0.09, 0.15, 0.10 10 550, 970 2450, 1830 20 22 1.47 1.5 22.5 0 Can’t I just round it to 2?

21. Temperature (°C) Ice Cream Sales ($) 0 Add adjusted scale each time 1.5 3.0 4.5 6.0 7.5 9.0 10.5 12.0 13.5 15.0 16.5 18.0

22. Part II: Determine the Scale for the following sets of data: ValuesRange # of boxes Range ÷ boxes Adjusted Scale Adjusted scale x # boxes Starting Value Ending Value = (Adjusted scale x # boxes) + starting value 4, 1, 0, 5, 7, 22 15 1.1, 0.95, 1.01, 1.09, 0.98 15 225, 331, 115, 45, 279 20 0.20, 0.04, 0.09, 0.15, 0.10 10 550, 970 2450, 1830 20 22 1.47 2 30 0 This will not spread out the data as much but …

23. Part II: Determine the Scale for the following sets of data: ValuesRange # of boxes Range ÷ boxes Adjusted Scale Adjusted scale x # boxes Starting Value Ending Value = (Adjusted scale x # boxes) + starting value 4, 1, 0, 5, 7, 22 15 1.1, 0.95, 1.01, 1.09, 0.98 15 225, 331, 115, 45, 279 20 0.20, 0.04, 0.09, 0.15, 0.10 10 550, 970 2450, 1830 20

24. ValuesRange # of boxes Range ÷ boxes Adjusted Scale Adjusted scale x # boxes Starting Value Ending Value = (Adjusted scale x # boxes) + starting value 4, 1, 0, 5, 7, 22 22151.47 1.5 22.5 0 2 30 0 1.1, 0.95, 1.01, 1.09, 0.98 0.15150.01 0.150.951.1 225, 331, 115, 45, 279 2862014.31530045345 0.20, 0.04, 0.09, 0.15, 0.10 0.16100.0160.020.2 00.20 0.040.22 550, 970 2450, 1830 1900209510020005002500

25. 5.Title the graph: Remember the title can be a clue as to what is shown by the slope of the line. The titles are usually written as “y vs x” (dependent variable vs independent variable). For example a graph of distance on the y is and time on the x axis can be titled “Graph of Distance vs. Time”. In this case, it would also be called “Graph of Speed”, since the slope of a distance vs. time graph represents speed.

26. Ice Cream Sales ($) Temperature (°C) Ice Cream Sales Vs.Temperature

27. 6.Plot: Put a dot at the location of each pair of variable values

28. Ice Cream Sales Vs.Temperature Ice Cream Sales ($) Temperature (°C) Ice Cream Sales vs Temperature Tempera ture °C Ice Cream Sales 14.2°$215 16.4°$325 11.9°$185 15.2°$332 18.5°$406 22.1°$522 19.4°$412 25.1°$614 23.4°$544 18.1°$421 22.6°$445 17.2°$408

29. 7.Draw the line or curve of best fit: We often want to find the “best fit line” straight line. To do this by hand, line up a ruler with the data points as best as you can, and draw a straight line. Roughly half of the points should be above the line, and half below it, in a random fashion. Do not force the line to go through the first and last data points. In fact, the line may not necessarily pass exactly through any of the data points. The line should reflect the general trend of the data as a whole, averaging out any random variations. Sometimes the data will show a curved relationship. Draw a smooth curve through the data points.

30. Ice Cream Sales Vs.Temperature Ice Cream Sales ($) Temperature (°C)

31. Draw a best fit curve or line

34. 8.If necessary determine the slope: Choose two points on the line, with coordinates (x1,y1) and (x2,y2), and calculate the slope m as:

35. The two points used in this calculation should not, in general, be actual data points. Also, they should be as far apart as possible, for maximum precision in calculating the slope. Do not restrict yourself to points where the best-fit line passes through an intersection of two gridlines.

36. Communicating what the graph reveals Interpreting Graphs: Explain in words what the graph shows. Types of relationships include: ____________________ relationship: Both factors (variables) increase or both factors (decrease) at a constant rate. Represented by a linear line. ___________________relationship: The factors change in opposite directions. One factor (variable) may increase while the other decreases. Both factors do not have to change at the same rate. Direct (linear) Inverse

37. Communicating what the graph reveals ____________________relationship: Factors increase sharply in both directions. Both factors do not have to change at the same rate. _________relationship: One (factor) variable will increase and the other (factor) variable does nothing at all. No increase or decrease. Exponential No

38. Which graph? Exponential Direct No relationship Inverse

40. Graphing Vocabulary __________________: extending the graph, along the same slope, above or below measured data. __________________: predicting data between two measured points on the graph

41. X Axis Y Axis Density

42. Graphing Vocabulary __________________: extending the graph, along the same slope, above or below measured data. __________________: predicting data between two measured points on the graph Extrapolate

43. X Axis Y Axis Temperature Density

44. Graphing Vocabulary __________________: extending the graph, along the same slope, above or below measured data. __________________: predicting data between two measured points on the graph Extrapolate Interpolate