Math 598: A Mean Course in Statistics
Datasets of the Day
Seattle Precipitation: Annual precipitation amounts for Seattle, WA from 1909-1997. Excel Format Minitab Format Classroom Use
Florida 2000 Presidential Election: Voter results by county for the 2000 election. Minitab Butterfly Ballot Classroom Use
Classroom Content Survey Results: The results of our classroom survey. Minitab (not meant for classroom use)
Penny Activity Data Excel Classroom Use
1969 Draft Data: The results of the 1969 draft lottery. high priority (001) to low (366) Minitab Classroom Use
German Temperature Data Summer and Annual averages for a 200 year period. Excel Classroom Use
Data for Excel Practice Excel
Soda Consumption Data on the amount of soda (diet and regular) consumed in US Excel Classroom Use
High School Sports Team Data Excel Classroom Use
Crude Oil and Gasoline Prices Excel Classroom Use
Cost to Rent Excel Classroom Use
Anscombe Correlation Data: Very different data with same regression line and r. Excel Minitab Classroom Use
Cheeseburger Nutrition Data Excel Classroom Use
Wage data for Educators Excel Classroom Use
Salmon at Bonneville (caution: profanity) Excel Classroom Use
Minimum Wage Excel Classroom Use
Basketball Trends Excel Classroom Use
Data needed for the Excel and Minitab practice:
Seattle Rainfall Data is from up above.
Caffeine data in Minitab and Excel format. See Detailed Description for information about both data sets.
Classroom Capsules
Description: Short lesson, clarification of concept
Topic: Standard deviation/normal distribution
Materials: Overhead sheet with normal distribution/standard deviation, markers
Description:
The following is a guided worksheet that would be used at the beginning of a pre-integrated class. The intent is to have students be able to collect their own data while remembering a few different types of graphing techniques. While this is simply the introduction to allowing us to gather our own statistical data, it reviews previous topics and is able to get students involved. In the next lesson, (perhaps “Classroom Capsule 2”) we will interpret the graphs and investigate traditional statistics such as mean, median and mode. This is innovative compared to other plans because the students get an interesting hands-on data set that is fun while informative.
Topic: Review of Graphing Techniques and Collection of Statistical Data (to be used later)
Resources: Enough fun-size bags of M&Ms candies for each student, Packet for each student, Colored pencils or crayons
Coin Data: Comparing Dates on Various Coins, Helping to Teach Histograms and Measures of Center and Spread
This classroom capsule is designed for a class of 30 students. It brings three activities together that revolve around the penny collection activity. These activities are to be performed independently from one another but in the following order:
Data analysis for the first activity will be performed using TI-83 calculators. The second activity will use Fathom. The third activity will use Excel.
Developing Binomial Probability with Pennies
Introduction to Non-Linear Regression and Modeling
This is an in-class activity students would complete in pairs. It requires the use of a TI-83 calculator (other graphing calculator or computer could be substituted). The activity is given to students when they have had some experience with linear regression and have been introduced to correlation. The goal of this activity is to introduce students to various non-linear regression models, and the process of deciding which model best fits a set of data. Students will need to take into consideration the fact that the regression equation used is modeling real data and the regression model that appears to fit may not actually be the best model.
In order to complete this activity, a classroom set of TI-83 calculators would be necessary, as well as an adaptor for overhead viewing. Students should also be given a list of regression types, their standard-form equations, and a picture of their graphs. This list should include linear, quadratic, cubic, quartic, logarithmic, exponential, power, logistic, and sinusoidal regression.
Measures of Central Tendency (more M&Ms) :This student activity is designed to engage students while learning measures of central tendency.
Another Letter Frequency Activity:
This is an in-class activity students would complete in groups of three. It requires students have access to random books; textbooks from other disciplines can be used. Students should have an understanding of how to calculate and work with percentages before completing this activity. The goal of this activity is to help students develop a better understanding of how to analyze mathematical information and to organize, clarify, and refine an argument. This activity will also introduce students to the process of systematic data gathering and how the data can be biased by the sources used. Students can complete the table and the class percentage in class and then complete the rest for homework with follow-up questions the next day. The teacher may want to make sure students have some understanding of the games Scrabble and Wheel of Fortune before students are left to complete the questions on their own.
TI-83 Calculator Lab: In this activity, students understand that evaporation rate is a characteristic property of a liquid. Based on this fact, they identify the solution and the likely accelerant in a case of arson. They compare the evaporation rates of the accelerants found with the suspects with those near the crime site. Page 1, Page 2, Page 3, Page 4.
Balancing Data is a student activity that introduces the mean as the balancing point in a data set. Students can use it to estimate the mean from a histogram verses calculating it.
Classroom Data: This classroom capsule is designed to be used during the first week of school. Students will each receive a slip of paper which will ask of them certain information (see attached worksheet). All data obtained from the students will be collected and entered into a master Excel worksheet. These data will serve two purposes. First, I will be able to use the data as a teaching tool to illustrate graphical and numerical analyses via my computer/projector setup. Secondly, students will analyze the data themselves using their TI-83 calculators (see attached worksheet).
Election Polls The activity is designed to have students analyze and interpret real-world data. I would have the above data displayed as the students enter the room and have them respond to the following questions in a journal entry, “Based on the White House 2008 General Elections polls, what candidate, would you expect to win the November election? Support your answer with data from the table.” Two of the statistical topics that I would hope the students recognize are sample size and margin of error. The only resource required is a projector.
Election Polls2: The activity is designed to have students see how statistics is used daily and show them that they should be informed consumers when it comes to the accepting data as it is presented to them. Two of the statistical topics that I want the students recognize are sample size and margin of error. Additionally, I want them to be conscience of the data that is presented to them and question whether they have enough information to be able to accept the results that have been reported.
Misleading Graphs: Topic: Misleading statistical interpretations introduction
Materials: Overhead sheets, overhead projector
Description: This is an activity that shows students that a simple random sample is the most effective way to estimate a population’s mean. The goal is also to show that people have bias and to avoid that bias statisticians use simple random samples.
Topic: Simple Random Samples
Resources: Each student will need a Jelly Blubber worksheet and a ruler.
Topics:
Random Sampling, Mean, Standard Deviation, Confidence Intervals
Goals:
- To engage students in developing statistical understanding about random sampling (They will be doing the sampling from various sources and need to decide what would make a good sample.)
- To increase understanding of confidence levels and what they measure.
- Incorporate cooperative learning in the classroom
Materials Needed:
Computer lab, Excel or Minitab
50 (more or less at your discretion) recent Washington newspaper classified sections…should be from several different areas in Washington State. These are available on line at: http://www.usnpl.com/wanews.php
Smiling and Leniency Study: Activity and Data
Content-: Explore case “Smile and leniency “following question:
Description:
This is a lesson plan with a worksheet and java applet that would be used at the beginning of a pre-integrated class. The goal of this lesson is to introduce the concepts of mean, median and mode and to develop understanding and familiarity with these ideas. The Mean and Median Activity lets students explore mean and median in an efficient way; the Mean, Median and Mode Discussion helps them to formalize their knowledge. To connect to CC1, have students find mean, median, and mode of each of the colors of m&m statistics gathered. Compare the relationship to mean, median and mode to the graphs constructed in CC1.
Description:
The following is a guided worksheet that would be used in an Algebra one course during a probably unit. This activity specifically focuses on proportional reasoning. The intent is to have students be able to collect “random” data with the assistance of the graphing calculator and use reasoning to determine the solution to the three outcomes posted on the activity.
Topic:
Probability and Odds: Proportional Reasoning
Resources:
Packet for each student
TI-83 for each student
Statistical Topic: Multiple Representations of Statistics and Outliers
This is an in-class activity students would complete in pairs or small groups. It requires the use of a TI-83 calculator (other graphing calculator or computer could be substituted). The activity is given to students when they have had some experience with graphical representations and have been introduced to the subject of outliers. The goal of this activity is for students to review several different representations commonly used and investigate what affect an outlier can have on those representations.
In order to complete this activity, a classroom set of TI-83 calculators would be helpful, as well as an adaptor for overhead viewing.
Matching Boxplots This worksheet has to do with matching histograms with box plots. The objective of this worksheet is to improve student’s ability to interpret information given in a boxplot, by matching box plots of sample data drawn from different distributions with their associated histograms.
Description:
This classroom capsule outlines the requirements and expectations of weekly I.P.O.D.S. (Individual Presentation Of Data by Students). Students will sign up for weekly demonstrations where they will use the teacher’s computer or document camera to present data of interest to them. Graphical and Statistical analysis of data will be required (see attached rubric).
Concepts
Materials
Technology Goals
Description: This activity is a curve fitting activity that has to do with the size of a diamond and its cost. This activity could be used as practice for students to use either a calculator or some other type of technology to fit a curve to this data.
Topic: Curve fitting (Regression)
Resources: Need the worksheet and some type of technology to plot the data.
Driving: Age and Weather : Activity and Data
Content-: Explore the case from links articles following question:
1. Is gender or age related to the likelihood of driving in inclement weather?
2. Does the number of accidents that someone thinks occur during inclement weather relate to how often he or she takes public transportation or chooses to drive during inclement weather?
What is the best beverage? Students will analyze beverage data and use technology to produce visual displays to create a convincing argument highlighting the best and worst of the beverage marketplace.
Description:
This activity is designed to help students to understand what makes a sample a good representation of the population. The worksheet at the end will be a tool for assessing the students understanding of Random Sampling.
Overview
This activity provides an opportunity to collect data from the internet, and perform data analysis employing capabilities of the TI-83/84.
Websites
Java Applets from Moreno's article (ch 4).
Nice Java Applets (I've just looked at the one for the Central Limit Theorem). Thanks to Colleen for finding this one.
Robin Lock's course page.
Guessing Correlations applet.
The CHANCE website: This is for designing an introductory probability/statistics course around current events in the news.
Against All Odds: Inside Statistics: nice video series on probability and statistics topics. Buy DVDs or watch for free.
Other Tidbits
A boxplot macro!!! Found on the website for Moore's book, The Basic Practice of Statistics
Information about the software FATHOM.
NPR article on the bias of coin tossing (a la Persi Diaconis). A press release from Stanford that has some interesting biographical tidbits. The paper.
Two videos: the UN Data presentation referred to in an edition of CHANCE News and just a bit of iphone humor (better then Mentos and soda).