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Information from
Samples
Alliance Class
January 17, 2012Math
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Agenda
Lessons for Student
Posters
CCSS Grade 7 StatisticsTypes of Sampling
Sampling Activities
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Lesson Plans for Student Posters
Day 1: Brainstorming 2/17
Day 2: Sort and Classify Questions 2/17
Day 3: Planning 2/17
Day 4: Data Collecting 3/17
Day 5: Graphs 3/17
Day 6: Poster 4/1 or spring breakMath
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WALT
1. Develop an understanding of 7.SP.1 and 2.
2. Understand the different methods of collecting a
sample from a population.
3. Understand the need for random selection of asample.
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Success Criteria
When I am able to clearly explain and provide an
example for CCSS standard 7.SP. 1and 2.
When I am able to identify the different methods of
sampling and explain why random sampling isimportant.
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CCSS 7thGrade Statistics
Domain
Use random sampling to draw inferencesabout a population.
1.Understand that statistics can be used to gaininformation about a population by examining asample of the population; generalizationsabout a population from a sample are validonly if the sample is representative of thatpopulation. Understand that random samplingtends to produce representative samples andsupport valid inferences.
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CCSS Grade 7 Statistics Domain
2. Use data from a random sample to drawinferences about a population with anunknown characteristic of interest. Generatemultiple samples (or simulated samples) ofthe same size to gauge the variation inestimates or predictions. For example,estimate the mean word length in a book by
randomly sampling words from the book;predict the winner of a school election basedon randomly sampled survey data. Gaugehow far off the estimate or prediction might
be.Math
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Standard 7.SP.1
Read Standard 7.SP.1
Divide your paper in
half. On one side,rephrase this standard
and on the other side,
provide an example.
Share with your
partner.
Standard 7.SP.1
Rephrased: Example:
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Standard 7.SP.2
Read standard 7.SP.2
Divide your paper in
half. On one side,rephrase this standard
and on the other side,
provide an example.
Share with your
partner. MathAlliance
Project
Standard 7.SP.2
Rephrased: Example:
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Types of Sampling
Simple Random Sample
Stratified Random Sample
Cluster sampling
Systematic
Convenience
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Simple Random Sample
Every subset of a specified size n from the
population has an equal chance of being selected
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Stratified Random Sample
The population is divided into two or more groups
called strata, according to some criterion, such as
geographic location, grade level, age, or income,
and subsamples are randomly selected from eachstrata.
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Cluster Sample
The population is divided into subgroups (clusters)
like families. A simple random sample is taken of
the subgroups and then all members of the cluster
selected are surveyed.
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Systematic Sample
Every kth member ( for example: every 10th
person) is selected from a list of all population
members.
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Convenience Sample
Selection of whichever individuals are easiest to
reach
It is done at the convenience of the researcher
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Errors in Sampling
Non-Observation Errors
Sampling error: naturally occurs
Coverage error: people sampled do not match the
population of interest Underrepresentation
Non-response: wont or cant participate
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Errors of Observation
Interview error- interaction between interviewerand person being surveyed
Respondent error: respondents have difficult time
answering the question Measurement error: inaccurate responses when
person doesnt understand question or poorlyworded question
Errors in data collection
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Random Rectangles
1. When given the cue turn the paper over.
Within 5 seconds make a guess for the
average area of the rectangles.2. When given the cue turn the paper over.
Select 5 rectangles you think are
representative of the rectangles on the page.
Write the rectangle numbers and their areas.Compute the average of the 5 rectangles.
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Random Rectangles
3. Use the random-number generator on the
graphing calculator to select five different
numbers from 1 to 100.
Write down the five numbers and the area ofeach of the five rectangles.
Find the area of the five rectangles.
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Random Rectangles
Report the three answers that you found for the
average of the rectangles.
1.Guess
2.Representative sample
3.Random sample
At your table construct 3 box plots
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Random Rectangles
Compare the three box plots. Describe any
similarities and differences.
Compare the medians of the three box plots to theactual area of all 100 rectangles.
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racticeAt your table explain how you would conduct:
A simple random sample of teachers in our class
A stratified random sample of teachers in our
class
A systematic sample of teachers in our class
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Practice
To conduct a survey of long-distance calling patterns, a researcheropens a telephone book to a random page, closes his eyes, putshis finger down on the page, and then reads off the next 50names. Which of the following are true statements?
I. The survey design incorporates chance
II. The procedure results in a simple random sampleIII. The procedure could easily result in selection bias
a) I and II
b) I and III
c) II and IIId) I, II and III
e) None of the above gives the complete set of true responses
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Practice
A large elementary school has 15
classrooms, with 24 children in each
classroom. A sample of 30 children is
chosen by the following procedure:
Each of the 15 teachers selects 2children from his or her classroom to
be in the sample by numbering the
children from 1 to 24, using a random
digit table to select two different
random numbers between 01 and 24.
The 2 children with those numbers are
in the sample.
Did this procedure give a simple random
sample of 30 children from the
elementary school?
a) No, because the teacherswere not selected randomly
b) No, because not all possiblegroups of 30 children had thesame chance of being
chosenc) No, because not all children
had the same chance ofbeing chosen
d) Yes, because each child hadthe same chance of being
chosene) Yes, because the numbers
were assigned randomly tothe children
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Visual Bias
Pull the slide until the line on the slide looks as if it
is the same length as the line on the face of the
card.
Turn the card over and read the length
Record this length and report it when asked.
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Bias Experiment
Report your length.
Construct a box plot of the class data.
Compare the box plot to the actual length.
Do the reported lengths tend to be the same? Do
they appear to be systematically too long or too
short?
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Homework
CMP Samples and Population (Handout)
Read pp. 26 to 32.
Do Problem 2.3 page 32
Use the spinners on page 31 and a paper clip as
the spinner to generate the random numbers that
are needed for A1 and 2.
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