1. Two Variable Data

2. Day 1 One-Variable vs. Two-Variable Data One-Variable Data measures one characteristic. This type of data is generally presented in one of the following ways:

3. One-Variable Data Tally Chart

4. One-Variable Data Frequency Table

5. One-Variable Data Bar Graph

6. One-Variable Data Histogram

7. One-Variable Data Pictogram

8. One-Variable Data Circle Graph

9. Two-Variable Data Two-variable Data measures two characteristics. This type of data is generally presented in one of the following ways:

10. Two-Variable Data Ordered Pairs

11. Two-Variable Data Scatter plot

12. Two-Variable Data Table of values

13. Example 1 Decide if the following is an example of one- variable or two-variable data a)Michael records the daily low temperature for the month of February. b)Pajas compares the amount of time she studies with the amount of time she sleeps each day.

14. Example 2 Identify the two variables used in the following data sets. a)Archeologists, through the use of DNA from bones, have determined that as more people began farming the more often they were sick and died. b)The faster the temperature increases in March the more likelihood of flooding.

15. Scatter Plots Scatter plots are a graphical and visual representation of data points. Each point on the scatter plot represents one part of a two-variable data set.

16. Dependent vs. Independent Not every data set has one variable that depends on another. When we have a variable that depends on the results of another we call this variable dependent. When we have a variable that does not depend on another we call this variable independent.

17. Example 1 Determine which variables are dependent and which are independent. a)The age of a car and the value of a car. b)The cost to do a job and the time it will take to complete the job. c)The total amount on a paycheque and the number of hours you worked.

18. Correlation If a relationship exists between two variables we say they are correlated or that a correlation exists. If two variables are correlated we generally see some kind of pattern in the scatter plot.

19. Correlation If one variable increases as the other also increases we say there is a positive correlation

20. Correlation If one variable decreases as the other increases we say there is a negative correlation.

21. Correlation If no pattern exists we say there is no correlation

22. Causation Observing a relationship between two variables does not mean that one variable causes a change in the other. Other factors could be involved or it could be coincidence.

23. Example 2 Determine if the findings are reasonable a)Serge discovered a positive correlation between gas price and average monthly temperature. He concluded that temperature determines the price of gasoline. b)Average household income has been steadily increasing in the last few decades. Crime rates have also increased. Does a higher household income cause people to commit more crime?

24. Homework Try page 133 #1a, 2a, 3, 5, 8 Try page 142 #3, 4, 5, 6, 8, 13

25. Day 2 Line of Best Fit A line of best fit is a line drawn through data points to best represent a linear relationship between two variables Generally a line of best fit should: ▫Pass through as many points as possible ▫Follow the trend in data ▫Have as close to equal number of points above and below the line.

26. Example 1 Is this a good line of best fit?

27. Example 1 Is this a good line of best fit?

28. Example 1 Is this a good line of best fit?

29. Example 1 Is this a good line of best fit?

30. Outlier A point that lies far away from the majority of other points is called an outlier. An outlier may be caused by inaccurate measurements or an unusual but valid result.

31. Making Predictions A line of best fit represents the average value and therefore can be used to make predictions. A prediction made within our set of data is called an interpolation. A prediction made outside our set of data is called an extrapolation.

32. Example 2

35. Reliability Data spread over a small interval is less reliable that data spread over a larger interval. When making predictions, the further from the main grouping of data the prediction is, the less reliable it is. The more data in a data set the more reliable a prediction will be.

36. Linear vs Non-linear When data increases/decreases at a similar pace a linear model might be a good fit. When data does not increase/decrease at a similar pace, a non-linear model might be a good fit.

37. Homework Try page 153 #1-3, 6, 7b, 8, 14

38. Day 3 Finding the Equation of the LOBF

39. Finding the Equation of the LOBF Generally the steps followed to find the equation are the following 1.Find the slope of the line 2.Substitute the slope into the eqn of the line 3.Substitute a point into the eqn of the line 4.Solve for b (the y-intercept) 5.Restate the equation with m and b inserted

40. Finding the Equation of the LOBF

41. Find the Line of Best for the Data

42. Finding the Equation of the LOBF Identify two points the LOBF passes through (1, 2.5) (6, 7)

43. Finding the Equation of the LOBF

46. Making Predictions Having the equation of the line of best fit can help us make predictions on what might happen in the future or what might have happened in the past. The more data we have will make our predictions more reliable.

47. Making Predictions Follow the steps discussed in class to find the predicted number of people charged with the following crimes in 2015. Is this an example of a interpolation or extrapolation? How reliable do you think the prediction is?

48. Making Predictions

49. Homework Try page 153 #9, either 10 or 11

50. Day 4 Scatterplots on Graphing Calculators The instructions can be found on page 160 of the textbook. Some important reminders. 1.To clear the memory: 2 nd + 7 1 2 2.To Enter a list of values: STAT 1 3.To show graph: 2 nd Y= 4.To show LOBF and eqn: STAT  2 nd 1, 2 nd 2, VARS  1 1 ENTER

51. Making Predictions

52. Scatterplots on Graphing Calculators Follow the instructions starting on page 159 to complete the activity. You can work with a partner. The following answers need to be handed in on a separate sheet of paper. 1ab, 2, 4, 5, 7, 10

53. Day 5 Statistical Literacy Definition: The mean is the average of a set of values. The mean is calculated by finding the sum of your data and dividing it by the number of values in the data.

54. Example 1 The following values are heights for a class of boys who are 13 years old (in cm). Determine the mean value. 161, 163, 159, 161, 165, 169, 172, 159, 160

55. Example 1

56. Statistical Literacy Definition: The median is the middle value of a set of data, when listed in order. Half the data is higher and half the data is lower than the median.

57. Example 2 Find the median of our previous set of data 161, 163, 159, 161, 165, 169, 172, 159, 160

58. Example 2 Find the median of our previous set of data 161, 163, 159, 161, 165, 169, 172, 159, 160 159, 159, 160, 161, 161, 163, 165, 169, 172 Since there are 9 pieces of data then the 5 th piece of data is the median.

59. Statistical Literacy Definition: The mode is the value(s) that are repeated most often. If all values are not repeated then there is no mode. There can be more than one mode.

60. Example 3 Find the mode of the previous set of data 161, 163, 159, 161, 165, 169, 172, 159, 160

61. Example 3 Find the mode of the previous set of data 161, 163, 159, 161, 165, 169, 172, 159, 160 Both 159 and 161 are repeated twice so they are both my mode.

62. Statistical Literacy Definition: The range is the difference between the largest and the smallest number in a data set.

63. Example 4 Find the range of our previous set of data 161, 163, 159, 161, 165, 169, 172, 159, 160

64. Example 4 Find the range of our previous set of data 161, 163, 159, 161, 165, 169, 172, 159, 160 Range = 172 – 159 Range = 13 cm

65. Percent Increase / Decrease Definition: A percent increase/decrease describes the change in a value as a percent based on the original value.

66. Example 5

69. Homework Try page 192 #1-3 Try page 193 #1, 2 Try page 194 #1, 2 Read page 195, do #1

70. Day 6 Interpreting Statistics Definition: A percentile tells approximately what percent of the data are less than a particular data value.

71. Example 1

72. Example 2

73. Quartile Definition: A Quartile is any of 3 numbers that separate a sorted data set into 4 equal parts.

74. Quartile The 2 nd quartile is the median since it cuts the data in half. It represents the 50 th percentile. The first (lowest) quartile is the median of the data values less than the median. This number represents the 25 th percentile The third (highest) quartile is the median of the data values more than the median. This number represents the 75 th percentile.

75. Example 2 continued

79. Conclusions Definition: A valid conclusion is one that is supported by unbiased data that has been interpreted appropriately.

80. Conclusions When you read a conclusion someone has made based on statistics, you must decide whether the conclusion is valid. To do this, ask yourself: Is there any bias in the data collection - in the way the sample was selected, the questions were phrased, or the survey was conducted? If the data involve measurements, were they accurate? Are any graphs drawn accurately or do they mislead the viewer?

81. Homework Try page 201 #1,3,7,8,9,14 Try page 229 #1,3,8,11

82. Day 7 Use and Misuse of Statistics In 2002 the BBC and Good Morning America claimed that the World Health Organization said that “blonde hair will become extinct by 2202” “We have no opinion on the future existence of blondes” WHO Why did this happen?

83. Use and Misuse of Statistics Sometimes media can exaggerate a number to give weight to an argument. John Stewart Ex. Million Man March – called this before it even happened. Major inaccuracy when estimating a crowd even close to 1 million in size.

84. Use and Misuse of Statistics Sometimes data can be selected in a way to support the argument they wish to make while underplaying or ignoring data that undermines it. President George Bush (8:15)President George Bush Scores in reading and math increased for students in grades 4 and 8 but decreased for students in grade 12 No analysis was reported about subject areas other than reading and math. Scores in grades 4 and 8 were increasing yearly before “No Child Left Behind” began.

85. Use and Misuse of Statistics Data can be manipulated to appear more favorable than it actually is. Quaker Oatmeal

86. Use and Misuse of Statistics In mid-1980s scientists notices a rise in brain tumors after NutraSweet was introduced. In the mid-1980s the number of MRI machines in the USA tripled, and Medicare began approving MRI scans for its patients.

87. Use and Misuse of Statistics Claims can be made on situational evidence instead of scientific studies Autism vs Vaccinations The U.S. Institute of Medicine (IOM) has conducted evidence-based reviews and has rejected any causal associations between the measles-mumps- rubella (MMR) vaccine and autism spectrum disorders in children. This is not the only evidence based study that has disproved any connection. Some speculation has tried to link thimerosal in the MMR vaccine to autism, but the MMR vaccine routinely used in Canada has never contained thimerosal. DTaP, polio and Hib vaccines have not contained this preservative since 1997-98. Although the reason for the increase in autism is not yet conclusively known, one explanation may be the broader definition and inclusion of many more behaviours and learning disorders within autistic spectrum disorders. It is relevant to consider the rise in autism in Denmark, even though the MMR vaccine preservative is banned there.

88. Day 8 Surveys and Questionnaires Definition: The sample size is the number of people or groups surveyed. If the sample is too small the results may be unreliable. If it is too big the survey becomes costly and difficult to administer.

89. Representative Sample Definition: A representative sample is a sample that is typical of the population. If it isn’t then the survey is biased (very likely)

90. Random Sample Definition: A random sample has each member of a population having an equal likelihood of being selected. A non-random sample may not yield a representative sample.

91. Types of Sampling There are many ways to choose the sample of the population to survey. Simple Random Sampling: individuals are chosen randomly from the entire population. Stratified Sampling: data are grouped and a few individuals from each group are selected randomly. Cluster Sampling: data are organized into representative groups and then one group is chosen as a sample. Systemic Sampling: Every n th individual is sampled.

92. Non-Random Techniques Convenience Sample: Individuals who are easy to sample are chosen. Voluntary Sampling: participants volunteer to be included in the sample.

93. Bias Definition: Bias is an emphasis on characteristics that are not typical of the entire population. Biased questions restrict people’s choices unnecessarily or use words that could influence people to answer in a certain way.

94. Homework Try page 214 #1, 2, 5, 16b

95. Day 9 Indices Indicies help predict trends. A price index for instance helps predict trends in prices. An index describes an item based on a base value measured at a particular time or in a particular place. Statics Canada tracks price changes using several different indicies. The Consumer Price Index (CPI) is one very important one.

96. CPI What is the base year for CPI? When was the cost of all goods about 25% more than the base cost? What was the CPI for clothing and footwear in Feb 2014? What does it mean? What is the percent change for Energy from Feb 2014 to Feb 2015? What does it mean? What is the percent change for Shelter from Feb 2014 to Feb 2015? What does it mean?

98. CPI What is the base year for CPI? 2002 When was the cost of all goods about 25% more than the base cost? Jan 2015 What was the CPI for clothing and footwear in Feb 2014? What does it mean? 89.3 What is the percent change for Energy from Feb 2014 to Feb 2015? What does it mean? -8.2 What is the percent change for Shelter from Feb 2014 to Feb 2015? What does it mean? 3.6

99. Comparing Cities The 2006 UBS Prices and Earnings report includes a comparison of clothing prices in 71 cities. a)What city is the base city? b)Which cities have index values less than the base? What does this tell you? c)How do clothing prices in Zurich and Hong Kong compare to New York? CityCPI Zurich115.6 Oslo114.4 Dublin97.5 New York100.0 Toronto73.8 Tokyo148.1 Rome87.5 Hong Kong75.0 Delhi43.8

100. Homework Page 237 #1-3, 7, 9, 12