1. 1.1 example these are prices for Internet service packages find the mean, median and mode determine what type of data this is create a suitable frequency table, stem and leaf plot and graph 13.60 15.60 17.20 16.00 17.50 18.6018.70 12.20 18.60 15.70 15.30 13.00 16.40 14.30 18.10 18.60 17.60 18.40 19.30 15.60 17.10 18.30 15.20 15.70 17.20 18.10 18.40 12.00 16.40 15.60

2. Answers to yesterday’s problem Mean = 494.30/30 = 16.50 Median = average of 15 th and 16 th numbers Median = (16.40 + 17.10)/2 = 16.75 Mode = 15.60 and 18.60  bimodal What type of data? numerical, so at least Interval data. It has an absolute starting point, so it is ratio data Given this, a histogram is appropriate

3. Frequency Table Class IntervalFrequency 12.00 – 12.992 13.00 – 13.992 14.00 – 14.991 15.00 – 15.997 16.00 – 16.993 17.00 – 17.995 18.00 – 18.999 19.00 – 19.991

4. Stem and Leaf Plot StemLeaf 12.20 00 13.60 00 14.30 15.60 70 30 60 20 70 60 16.00 40 40 17.20 50 60 10 20 18.60 70 60 10 60 40 30 10 40 19.30

5. Histogram How many class intervals? What does the height of each bar mean? What does the histogram tell us about the data?

6. Trends in Data Chapter 1.3 – Visualizing Trends Mathematics of Data Management (Nelson) MDM 4U

7. Variables A variable is a symbol that represents an unknown quantity. In statistics, variables refer to measurable attributes. They can be:  Discrete (a single value)  Continuous (a range of values) A constant is known and unchanging  Ex. The boiling point of water

8. Two Types of Variables Independent Variable  placed on the horizontal axis  time is always independent (why?) Dependent Variable  values depend on the independent variable  placed on the vertical axis  Usually the variable you want to study

9. Trends a trend indicates a correlation that may be:  strong or weak  positive or negative  linear or non-linear

10. What is a trend? a pattern of average behavior that occurs over time a general “direction” that something tends toward need two variables to exhibit a trend

11. An Example of a trend U.S. population from 1780 to 1960 what is the trend? is the trend linear?

12. Line of Best Fit a line that best represents the trend in the data and is used for making predictions can be drawn by hand, but is more reliable if created mathematically gives no indication of the strength of the trend

13. An example of the line of best fit this is temperature data from New York over time, with a trend line added what type of trend are we looking at?

14. Creating a Trend Line on Excel Using the following games won data for the Montreal Canadiens, construct a scatter chart in Excel or Google Sheets Figure out how to make a linear trend line for the data and display the equation for the line Using the trend line, how many games can you estimate that the Canadiens might win in 2015-2016? 2016-2017? SeasonGames won 2010-201144 2011-201231 2012-201329 2013-201446 2014-201550

15. MSIP / Homework Complete p. 37 #2, 3, 6, 8

16. Trends in Data Using Technology Chapter 1.4 – Trends in Technology Mathematics of Data Management (Nelson) MDM 4U

17. Categories of Correlation From last class:  correlation can be positive or negative, strong or weak There can also be no correlation between two variables

18. Regression a process of fitting a line or curve to a set of data if a line is used, it is linear regression if a curve is used, it may be quadratic regression, cubic regression, etc. what can we do with the resulting function?

19. Correlation Coefficient the correlation coefficient, r, indicates the strength and direction of a linear relationship  r = 0no relationship  r = 1perfect positive correlation  r = -1perfect negative correlation r 2 is the coefficient of determination  if r 2 = 0.42, that means that 42% of the variation in y is due to x

20. NHL player height vs weight Pick 20 random NHL players Find out their heights and weights Create a scatter plot on your computer, along with a trend line Find the equation of the trend line and the r 2 value Describe the trend in terms of:  Positive vs negative  Strong vs weak  Linear vs non-linear

21. MSIP / Homework Complete p. 51 #1-6, 7 bcd, 8