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Statistics “Collect Data”

Math Teacher Leader SeminarDecember 6 & 13, 2007

Henry KepnerKevin McLeodDeAnn HuinkerConnie LaughlinKaren CorlynLee Ann PruskePaige RichardsMary Mooney

This material was developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under Grant No. 0314898. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the Foundation.

Session Goals

Examine Part II – Collect Data of the GAISE Framework for Statistical Problem Solving.

Explore the role of collecting data and the implications of how the data is gathered.

Explore concepts of bias and randomness.

Developed by the Milwaukee Mathematics Partnership (MMP) 2with support by the National Science Foundation under Grant No. 0314898.

A Framework for Statistical Problem Solving

GAISE Report (2007)

I. Formulate Questions

II. Collect Data

III. Analyze Data

IV. Interpret Results

GAISE: Guidelines for Assessment and Instruction in Statistics Education


A Fifth Grade Task

An elementary school with grades 1 through 6 has 100 students in each grade. A fifth-grade class is trying to raise some money to go on a field trip to the Wisconsin Dells. They are considering several options to raise money and decide to do a survey to help them determine the best way to raise the most money. One option is to sell raffle tickets for an Xbox 360 game system.

How could they find out whether or not students were interested in buying a raffle ticket to win the game system?

Source: Sowder, J., Sowder, L., & Nickerson, S. (2007). Reconceptualizing Mathematics. New York: W. H. Freeman.


How might you go about collecting data to answer this question? Individually, jot down your ideas.

Turn & Talk:Turn to others in your group and share your ideas.


What are some reasons for using a sample?

Why might we not want to ask everyone in the school?

Sample: A sample is the part of the population that is actually used to collect data. It is a subset of a population.

Population: A population is the entire group that is of interest.


Nine different students each conducted a survey to estimate how many students in the school would buy a raffle ticket to win an Xbox 360. Each survey included 60 students. Each student’s suggested technique is described on one of the cards in the envelope.

Directions:

1. Remove a card from the envelope.2. Read it to the table group.3. Answer the discussion questions.4. Pass the envelope repeat with a new

card.


Discussion Questions

In what ways is this sample representative of the entire student population?

In what ways is this not a representative sample of the entire student population?

Which plan will help us make the most informed decision?

How confident will you be in making a decision based on this data?

(Note in all cases, yes means that the student agreed to buy a raffle ticket.)


Raffi asked 60 friends. (25% yes, 75% no)

Shannon got the names of all 600 students in the school, put them in a hat, and pulled out 60 of them. (35% yes, 65% no)

Spence had blond hair so he asked the first 60 students he found who had blond hair. (55% yes, 55% no)

Jake asked 60 students at an after-school meeting of the Games Club. The Games Club met once a week and played different games- especially computerized ones. Anyone interested in games could join. (90% yes, 10% no)

Abby sent out a questionnaire to every student in the school and then she used the first 60 that were returned to her. (50% yes, 50% no)


Claire set up a booth outside the lunch room, and anyone who wanted to could stop by and fill out her survey. To advertise her survey, she had a sign that said WIN AN XBOX. She stopped collecting surveys when she got 60 completed. (100% yes)

Brooke asked the first 60 students she found whose phone number ended in a 3 because 3 is her favorite number. (25% yes, 75% no)

Kyle wanted the same number of boys and girls and some students from each grade. So he asked 5 boys and 5 girls from each grade to get his total of 60 students. (30% yes, 70% no)

Courtney didn’t know many boys so she decided to ask 60 girls. But she wanted to make sure she got some young girls and some older ones so she asked 10 girls from each grade. (10% yes, 90% no)


What does the word, bias, mean?

Bias

A sample is biased if the process of gathering the data makes it likely that the sample will not reflect the population of interest.

Bias occurs when a sample of a population systematically favors certain outcomes.


As a group, sort your cards along a continuum, ranking them as to your level of confidence from biased to unbiased.

Remember we want a representative sample of the entire population so we can be confident in our survey result.

Biased Unbiased


Randomness

Turn & Talk

What does it mean when something is random?

Why does randomness mean a less biased sample?

Should we have more confidence in a sample if randomness is involved?


Randomness

Randomness consistently used, neither over or underestimates the entire population’s results.


Sampling Techniques

Simple Random Sample

Stratified Random Sample

Systematic Sample

Convenience Sample

Voluntary Sample


Sampling Techniques

Simple Random Sample: A sample in which every element in the population has an equal chance of being selected for the sample and the selection of one element has no effect on the selection of any other element.Stratified Random Sample: The population is divided by a classification (strata), and then random samples are selected from each group.Systematic Sample: A sample generated by consistently selecting by using a pattern or identifiable characteristic. Convenience Sample: A group of people who are readily available are sampled.Voluntary Response Sample: The sample is drawn from people who voluntarily answer the question.


Turn & Talk:Reflecting on today’s session, collecting data with students, how might this information be used with K-2 students, with 3-5 students, and with 6-8 students?

Chart:

At your table, chart one idea for each of the grade level groupings. (We will collect and compile your suggestions.)


MPS Learning Targets

Descriptors(Kindergarten)

Sub-skill E.a: Data analysis and statistics

4). Using the context of the data, read and report results and answer questions.

MPS Learning Target #7(Grade 2)

Pose and answer questions about real-world situations by collecting and displaying data from surveys and experiments (e.g., spinners), and draw reasonable conclusions including the likelihood of events.

MPS Learning Target #7 (Grade 3)

Formulate questions that lead to real-world data investigations, collect, organize, and display data, and draw reasonable conclusions based on the data.

MPS Learning Target #4(Grade 8)

Design and conduct investigations, display data using appropriate representations, analyze and summarize data using measures of central tendency and variation, and evaluate methods and conclusions.


Mathematics FrameworkMilwaukee Public Schools


Big Ideas Finding a representative sample is

extremely important in deriving statistics that can be used in making decisions.

A result from a relatively small, but carefully chosen, sample can give information about the whole population.

A sample always refers to some subset of a population.

Randomness consistently used, neither over or underestimates the entire population’s results


DefinitionsPopulation: A population is the entire group that is of interest.

Sample: A sample is the part of the population that is actually used to collect data. It is a subset of a population.

Sample Statistic: A sample statistic is the result of a calculation (or count) based on data gathered from a sample.

Population Parameter: The same calculation based on the entire population is called a population parameter.

Biased Sample: A sample is biased of the process of the gathering the sample makes it likely that the sample will not reflect the population of interest.


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