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 graph13.60 15.60 17.20 16.00 17.50 18.60 18.7012.20 18.60 15.70 15.30 13.00 16.40 14.3018.10 18.60 17.60 18.40 19.30 15.60 17.1018.30 15.20 15.70 17.20 18.10 18.40 12.0016.40 15.60

Answers to yesterday’s problem Mean = 494.30/30 = 16.50 Median = average of 15th and 16th 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

Frequency Table

Class Interval Frequency

12.00 – 12.99 2

13.00 – 13.99 2

14.00 – 14.99 1

15.00 – 15.99 7

16.00 – 16.99 3

17.00 – 17.99 5

18.00 – 18.99 9

19.00 – 19.99 1

Stem and Leaf Plot

Stem Leaf

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

Histogram

How many class intervals?

What does the height of each bar mean?

What does the histogram tell us about the data?

1

2

3

4

5

6

7

8

10 12 14 16 18 20 22 24

Price

Internet Prices Histogram

Trends in Data

Chapter 1.3 – Visualizing Trends

Mathematics of Data Management (Nelson)

MDM 4U

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

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

Trends

a trend indicates a correlation that may be: strong or weak

positive or negative

linear or non-linear

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

An Example of a trend

U.S. population from 1780 to 1960

what is the trend?

is the trend linear?

Att

r2_

po

pm

illio

ns

0

20

40

60

80

100

120

140

PearlReedandKish1940_USpopulationfrom17901940_year1780 1800 1820 1840 1860 1880 1900 1920 1940 1960

019 Scatter Plot

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

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?

Att

r2_

me

an

tem

p

14

1618

20

22

24

2628

30

32

StateofNewYorkHistoricalTemperatureData_winters...1900 1920 1940 1960 1980 2000

Attr2_meantemp = 0.0230StateofNewYorkHistoricalTemperatureData_winterseasonmeanof40wea_ - 21.4

048 Scatter Plot

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?

Season Games won

2010-2011 44

2011-2012 31

2012-2013 29

2013-2014 46

2014-2015 50

MSIP / Homework

Complete p. 37 #2, 3, 6, 8

Trends in Data Using Technology

Chapter 1.4 – Trends in Technology

Mathematics of Data Management (Nelson)

MDM 4U

Categories of Correlation From last class:

correlation can be positive or negative, strong or weak

There can also be no correlation between two variables

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?

Correlation Coefficient

the correlation coefficient, r, indicates the strength and direction of a linear relationship r = 0 no relationship r = 1 perfect positive correlation r = -1 perfect negative correlation

r2 is the coefficient of determination if r2 = 0.42, that means that 42% of the variation in

y is due to x

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 r2 value Describe the trend in terms of:

Positive vs negative Strong vs weak Linear vs non-linear

MSIP / Homework

Complete p. 51 #1-6, 7 bcd, 8