MATH 598: Statistics & Modeling for Teachers

May 21, 2014

Agenda◦Pretest◦Big Idea Warm-up◦Introduction ◦M&Ms Activity

Warm-Up

◦Find someone with whom you did not work last week.

◦Spend 5 minutes discussing the following with your partner. Be prepared to summarize your discussion for the larger group: Which of the concepts included in Big Idea 1

do your students seem to understand well? Which of the concepts included in Big Idea 1

are more of a challenge for your students?

Formulate a question Gather data accordingly

◦ Design: plan on how to obtain data to answer the question of interest

Analyze data accordingly◦ Description: summarize and analyze the data that are

obtained Interpret results to answer the question

◦ Inference: make decisions and predictions based on the data for answering the statistical questions, typically we want to do this for a larger group than those directly in the study

Statistical Process

What proportion of students at your school prefer country music over rap, rock, and oldies?

How would you plan to gather data for this question?

We typically work with and observe samples but we are actually interested in populations

A population is the set of ALL the subjects of interest

In practice, we have data for only some of the subjects in the population

A sample is a subset of the population for whom we have (or plan to have) data, hopefully they are randomly selected

Occasionally, data are available for the entire population (e.g., Census)

Sample vs. Population

Descriptive statistics: methods for summarizing the collected data

Typically either a numeric summary (e.g., the mean) or a graph (e.g., a histogram)

Describing Data

A parameter is a numerical summary of the population

A statistic is a numerical summary of the sample

For example, suppose you are interested in the average grades of students at LMU and you take a sample of students to work with◦ What is the population of interest? ◦ What is the parameter of interest?◦ What is the sample statistic you would use?

Sample Statistic vs. Population Parameter

What proportion of students at your school state that country music is their favorite instead of rap, rock, and oldies?

◦ What is the population?◦ What is the population parameter of interest?◦ How could you investigate the population

parameter of interest?◦ Since the value of the sample statistic will vary for

each sample, how can you answer the question?

Return to our question:

Problem: How can we describe how the percentage of candies that are blue varies from one bag of M&Ms to another?

Launch

Get into groups of 2. Spend a few minutes discussing answers to the following questions.

1. What is the specific question that needs to be addressed in the investigation?

2. How does this question relate to the background information at the beginning of the activity? Be sure to use some of the review terms in your answer.

3. What is the population of interest in the investigation?4. What is the population parameter of interest in the

investigation?5. Why can we not realistically calculate the population parameter

of interest directly?6. How could the concept of random sampling be used to

investigate the population parameter of interest?

Questions

Each person will be given M&M bags. Record the number of blue M&Ms and

the total M&Ms in the bag for each of the bags.

Follow the activity sheet.

Sampling

What are the important take-away ideas from this task?

Follow-up

How might you extend this activity to build students’ understanding of sampling distributions?

Extensions

Which GAISE level is the M&Ms Activity? Which Common Core content standards are

addressed in the M&Ms Activity? Which Common Core mathematical practice

standards are addressed in the M&Ms Activity?

GAISE & Common Core

Take time to answer the set of in-class problems

In-class Problems

Bring your laptop to class. HW 2: Valentines Day Marbles

◦ Keep in mind that your work will be scored and returned to you. So, please write out complete answers. In other words, answer the questions in the manner that you would hope your students would.

◦ You should work alone.◦ Be prepared to share your answers with the rest

of the class. Read Big Idea 4 from 6-8 DEU

For Next Week