CCSS – STATISTICS THREADLOUISVILLE, KY 2012

Lisa Fisher-Comfort, MN Regional Coordinator, Michael Long, HI Regional Coordinator

Earlier in Chapter 4…

Lesson 4.2.1 Math Notes

Lesson 6.1.1 - Closure

Residuals

Battle Creek Cereal Scatterplot

Lesson 6.1.2 - Closure The first step in any statistical analysis is to graph the

data. Graphs do not necessarily start at the origin; indeed, frequently in statistical analyses they do not.

A residual is a measure of how far our prediction using the best-fit model is from what was actually observed.

A residual has the same units as the y-axis. A residual can be graphed with a vertical segment. The

length of this segment (in the units of the y-axis) is the residual.

A positive residual means the actual observed y-value of a piece of data is greater than the y‑value that was predicted by the LSRL.

A negative residual means the actual data is less than predicted.

Extrapolation of a statistical model can lead to nonsensical results.

The following table shows data for one season of the El Toro professional basketball team. El Toro team member Antonio Kusoc was inadvertently left off of the list. Antonio Kusoc played for 2103 minutes. We would like to predict how many points he scored in the season.

Player Name Minutes Played Total Points Scored in a Season

Sordan, Scottie 3090 2491Lippen, Mike 2825 1496Karper, Don 1886 594Shortley, Luc 1641 564Gerr, Bill 1919 688Jodman, Dennis 2088 351Kennington, Steve 1065 376Bailey, John 7 5Bookler, Jack 740 278Dimkins, Rickie 685 216Edwards, Jason 274 98Gaffey, James 545 182Black, Sandy 671 185Talley, Dan 191 36

checksum 17627 checksum 7560

Your Task (6-30)a.Obtain a Lesson 6.1.4 Resource Page from your

teacher. Draw a line of best fit for the data and then use it to write an equation that models the relationship between total points in the season and minutes played.

b. Which data point is an outlier for this data? Whose data does that point represent? What is his residual?

c.Would a player be more proud of a negative or positive residual?

d. Predict how many points Antonio Kusoc made.

LSRL on a Calculator6-33. A least squares regression line (LSRL) is a

unique line that has the smallest possible value for the sum of the squares of the residuals.

a.Your teacher will show you how to use your calculator to make a scatterplot. (Graphing calculator instructions can also be downloaded from www.cpm.org/technology.) Be sure to use the checksum at the bottom of the table in problem 6-30 to verify that you entered the data into your calculator accurately.

b. Your teacher will show you how to find the LSRL and graph it on your calculator. Sketch your scatterplot and LSRL on your paper.

Lesson 6.1.4 - Closure This is a two-day lesson. Problem 6-34 is

a Least Squares Demo that can be teacher led to summarize their understanding of Least Square Regression Lines.

LeastSquaresDemo.html

Find the Correlation Coefficient for the El Toro Basketball team

Describe the form, direction, strength, and outliers of the association.

Form could be linear but the residual plot indicates a another model might be better.

Direction is negative with a slope of 0.59; an increase of one minutes played produced 0.59 points scored on the average.

Strength is a fairly strong and positive linear association because r = 0.865.

Outliers: Scottie Sordan (a.k.a. Michael Jordan).

Lesson 6.2.2 ClosureComputer Exploration of Correlation Coefficients

Problem 6-72Students are asked to create scatterplots with

the following associations and record r:Strong positive linear associationWeak positive linear associationStrong negative linear association No linear association (random scatter)

http://illuminations.nctm.org/LessonDetail.aspx?ID=L456#first

21 San Francisco, CA 67 6722 Sacramento, CA 71 6823 Los Angeles, CA 71 6924 Raleigh, NC 63 7025 Des Moines, IA 72 7326 Kansas City, MO 73 7427 Chicago, IL 60 7528 Oklahoma City, OK 76 7629 Louisville, KY 70 7630 Topeka, KS 74 7731 Atlanta, GA 66 7932 Orlando, FL 79 8233 Baton Rouge, LA 81 8434 Honolulu, HI 84 8535 New Orleans, LA 80 86

High-Temperature DataCity 1975 (°F) 2000 (°F)

1 Anchorage, AK 13 332 Spokane, WA 52 443 Billings, MT 62 444 Juneau, AK 29 455 Bangor, ME 53 486 Bellingham, WA 52 537 Albuquerque, NM 67 538 Denver, CO 60 549 Portland, OR 57 54

10 Seattle, WA 54 54

11 Boston, MA 60 56

12 New York, NY 56 58

13 Duluth, MN 55 60

14 Bismarck, ND 66 61

15 Baltimore, MD 61 62

16 Washington, D.C. 62 62

17 Philadelphia, PA 59 62

18 El Paso, TX 83 65

19 Lansing, MI 55 66

20 Phoenix, AZ 77 67

Displaying Temperatures Is the planet getting hotter? Experts look at the temperature of the air

and the oceans, the kinds of molecules in the atmosphere, and many other kinds of data to try to determine how the earth is changing. However, sometimes the same data can lead to different conclusions because of how the data is represented.

Your teacher will provide you with temperature data from November 1, 1975, and from November 1, 2000. To make sense of this data, you will first need to organize it in a useful way. Your teacher will assign you a city and give you two sticky notes. Label the

appropriately colored sticky note with the name of the city and its temperature in 1975. Label the other sticky note with its city name and temperature in 2000.

Follow the directions of your teacher to place your sticky notes on the class histogram. Use the axis at the bottom of the graph to place your sticky note.

How many cities were measured for this study? Describe the spread and shape of each of the histograms that you have

created. Which measure of central tendency would you use to describe a typical temperature for each year? Justify your choice.

http://www.almanac.com/weather

Histograms and World Temperatures

Boxplots and Temperatures The histograms your class made in problem 8-44 display data along the

horizontal axis. Another way to display the data is to form a box plot, which divides the data into four equal parts, or quartiles. To create a box plot, follow the steps below with the class or in your team. With a sticky dot provided by your teacher, plot the 1975 temperature for your

city on a number line in front of the class. What is the median temperature for 1975? Place a vertical line segment about

one-half inch long marking this position above the number line on your resource page.

How far does the data extend from the median? That is, what are the minimum and maximum temperatures in 1975? Place vertical line segments marking these positions above the number line.

The median splits the data into two sets: those that come before it and those that come after it when the data is ordered from least to greatest, like it is on the number line. Find the median of the lower set (called the first quartile). Mark the first quartile with a vertical line segment above the number line.

Look at the temperatures that come after the median on your number line. The median of this portion of data is called the third quartile. Mark the third quartile with a vertical line segment above the number line.

Draw a box that contains all of the data points between the first and third quartiles. Your graph should be similar to a box with outer segments like the one shown below.

What does the box plot tell you about the temperatures of the cities in 1975 that the dot plot did not?

Two-day lesson Students use center, shape, spread and

outliers to compare two sets of numerical data.

Box Plots and Histograms

8-30. Mrs. Ross is the school basketball coach. She wants to compare the scoring results for her team from two different games. The number of points scored by each player in each of the games are shown below.

Game 1: 12, 10, 10, 8, 11, 4, 10, 14, 12, 9Game 2: 7, 14, 11, 12, 8, 13, 9, 14, 4, 8

a. How many total players are on the team? b. What is the mean number of points per player for each game? c. What is the median number of points per player for each game? d. What is the range of points scored by each player for each game? e. With your team, discuss and find another method for comparing the data. f. Do you think the scoring in two games is equivalent?

Follow Up Question

Math Notes

One method for measuring the spread (variability) in a set of data

is to calculate the average distance each data point is from the mean. This distance is called the mean absolute deviation. Since the calculation is based on the mean, it is best to use this measure of spread when the distribution is symmetric.

For example, the points shown below left are not spread very far from the mean. There is not a lot of variability. The points have a small average distance from the mean, and therefore a small mean absolute deviation. The points above right are spread far from the mean. There is more variability. They have a large average distance from the mean, and therefore a large mean absolute deviation.

ETHODS AND MEANINGS M

ATH

NOTE

S Mean Absolute Deviation

mean

x x x x mean

x x x

Mean Absolute DeviationData from Game 1: 12, 10, 10, 8, 11, 4, 10, 14, 12, 9

New tool – Standard Deviation

Standard Deviation Data from 11-60

Sugar W: 10, 32, 32, 34, 34, 36, 37, 39, 39, 40, 41, 43, 43, 44, 45, 46, 46, 49, 70 checksum 760