3. Example: Counting Apples

4. Tally Marks

5. You tally now!

6. Frequency Table

7. What type of jobs use frequency tables?

8. EXAMPLE

9. The marks awarded for an assignment set for a Year 8 class of 20 students were as follows: 6 7 5 7 7 8 7 6 9 7 4 10 6 8 8 9 5 6 4 8 Present this information in a frequency table. Step 1 Step 2 Step 3 Now you try! Page 17 Question 1!

10. Solutions to Exercise 1.3 Result 3 Heads 2 Heads 1 Head 0 Heads Tally Frequency 3 11 9 2

12. Stem-and-Leaf Diagrams and Stemplots A S & L diagram represents data by seperating each value into two parts: the stem (usually the leftmost digit) and the leaf. S & L diagrams represent data in a similiar way to bar charts. In stem-and-leaf plots, numeric data is shown by using the actual numerals. Stem-and-leaf plots are especially useful when you have a lot of data that has a wide range.

13. To make a Stemplot, follow these steps: The following stem-and-leaf plot shows the record of wins for the Eastern Conference NBA teams:

14. Back-to-Back S & L This S & L Diagram compares two data sets.

15. Histograms H. break the range of values of a variable into classes and display only the count or per cent of the observations that fall into each class. H. are used to represent CONTINUOUS NUMERICAL DATA!

16. The following frequency table shows the times, in minutes, spent by a group of woman in a boutique. Draw a histogram of the distribution. Time 0-10 10-20 20-30 30-40 40-50 Numbe r 1 4 8 7 9

17. Distribution of Data

18. Symmetric Distribution If the values smaller and larger than its midpoint are mirror images of each other

19. Negatively Skewered Distribution Also known as a skewered left distribution.

20. Positively Skewered Distribution Also known as a skewered right distribution.

21. What are Variables? Variables are things that we measure, control, or manipulate in research. They differ in many respects, most notably in the role they are given in our research and in the type of measures that can be applied to them. Variables are things that we measure, control, or manipulate in research. They differ in many respects, most notably in the role they are given in our research and in the type of measures that can be applied to them.

24. News Reporters love to tell stories about the latest links! Such as.. Does having her first baby later in life cause a woman to live longer? (New York Times) Do we believe this or much of anything anymore?

25. ‘ Count Cricket Chirps to Gauge Temperature’ ( Garden Gate ) ) What you have to do! 1. find a cricket 2. count the number of times it chirps in 15 seconds 3. add 40 You’ve just predicted the temp. in degrees Fahrenfeit!

27. Table 18-1 Cricket Chirps and Temperature Data (Excerpt) No. of Chirps in 15 sec Temperature (in degrees Fahrenheit) 18 57 20 60 21 64 23 65 27 68 30 71 34 74 39 77

28. To make a Stemplot, follow these steps: The following stem-and-leaf plot shows the record of wins for the Eastern Conference NBA teams:

29. Bivariate Data

31. Lets see another example!

32. A Press Release by Ohio State University Medical Center The headline says that... “ aspirin can prevent polyps in colon cancer patients”

35. Scatter Plot of cricket chirps versus outdoor temperature.

40. Positive Linear Relationship as the cricket chirps increase so does the temperature aswell.

41. Q. 3 Page 6 AQA GSCE Age of Car Value of Car (£)

42. Q. 4

43. Q 5. Point A B C D E F G H I J Days abs ent 1 2 3 4 5 6 7 8 9 10 No. of peop p 30 50 36 8 36 28 16 58 34 42

44. Q. 6

45. Q. 7

47. We have already seen how to measure the direction of a linear relationship BUT you will also have to decide on the STRENGTH of the relationsbip!! Introduce the...

51. Types of Correlation

52. It is important you state the Direction and the Strength of a Correlation Correlation Coefficient = 0.99 Correlation coefficient = 0.5

53. A positive correlation means that high values of one variable are associated with high values of a second variable . The relationship between height and weight, between IQ scores and achievement test scores, and between self-concept and grades are examples of positive correlation.

54. Correlation Coefficient = - 0.99 Correlation Coefficient = - 0.5

55. A negative correlation or relationship means that high values of one variable are associated with low values of a second variable. Examples of negative correlations include those between exercise and heart failure, between successful test performance and feelings of incompetence, and between absence from school and school achievement.

56. No CORRELATION Correlation Coefficient = -.16

57. 8.2 Scatter Plots Aus. Book Q. 3

58. Q. 4

59. Q. 7

60. Using your calculator to calculate the C.C!

61. Correlation Coefficient Before doing this on the calculator, the class should do a scatter graph using the data in the table. Discuss the relationship between the data (i.e. gms of fat v calories). Project Maths Development Team © 2008 Total Fat (g) Total Calories Hamburger 9 260 Cheeseburger 13 320 Quarter Pounder 21 420 Quarter Pounder with Cheese 30 530 Big Mac 31 560 Special 31 550 Special with Bacon 34 590 Crispy Chicken 25 500 Fish Fillet 28 560 Grilled Chicken 20 440 Grilled Chicken Light 5 300

63. SHARP EL-W531 Mode 1 1 2 (x,y) 5 DATA 12 (x,y) 24 DATA 21 (x,y) 24 DATA 15 (x,y) 25 DATA RCL r x y 2 2 12 21 21 21 15 5 5 24 40 40 40 25

64. Correlation Coefficient by Calculator This will show the table on the right on the screen. When all the data items are inputted, press the following: This will give a correlatrion coefficient of 0.9746 Compare this answer with your interpretation of the scatter graph. Using the Casio fx-83ES Project Maths Development Team © 2008 Now input all the data items into the X and Y columns. Press after each data item.

65. Scatter Plot of cricket chirps versus outdoor temperature.

66. Correlation of 0.98!

67. Correlation versus Causation

71. NO!!!! Production Costs Decreased Cost of Production was a third variable causing the other two to increase. We call this third variable a LURKING VARIABLE.

75. Because you have a strong correlation be it positive or negative you know that x is correlated with y. If you know the slope and the y-intercept of that line, then you can plug in a value for x and predict the average value for y. In other words, you can predict y from x. You should never do a regression analysis unless you’ve already found a strong correlation (either pos. or neg.) between the two variables!

79. Step 1

80. Step 2

81. Step 3

82. Step 4

83. Step 5

84. Now Calculate Line! i.e. what is the formula for the line? i.e. what is the formula for the line?

86. Q. 3 AQA GSCE

87. Q. 5

88. Q. 6

89. Q. 9 Active Maths 0.98

90. Q. 10 0.90

91. Exercise 1.7 QUESTION 4 (ii)0.96 (iii) Strong Positive Correlation (v) y = 4x + 6 (vi) € 18, 000