Information from
Samples
Alliance Class
January 17, 2012
Math
Alliance
Project
Agenda
Lessons for Student
Posters
CCSS Grade 7 Statistics
Types of Sampling
Sampling Activities
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Alliance
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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 break
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Alliance
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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 a
sample.
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Alliance
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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 is
important.
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Alliance
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CCSS 7th Grade Statistics
Domain
Use random sampling to draw inferences
about a population.
1. Understand that statistics can be used to gain
information about a population by examining a
sample of the population; generalizations
about a population from a sample are valid
only if the sample is representative of that
population. Understand that random sampling
tends to produce representative samples and
support valid inferences.
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Alliance
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CCSS Grade 7 Statistics Domain
2. Use data from a random sample to draw
inferences about a population with an
unknown characteristic of interest. Generate
multiple samples (or simulated samples) of
the same size to gauge the variation in
estimates 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 based
on randomly sampled survey data. Gauge
how far off the estimate or prediction might
be.
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Alliance
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Standard 7.SP.1
 Read Standard 7.SP.1
Standard 7.SP.1
Rephrased:
Example:
 Divide your paper in
half. On one side,
rephrase this standard
and on the other side,
provide an example.
 Share with your
partner.
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Alliance
Project
Standard 7.SP.2
 Read standard 7.SP.2
Standard 7.SP.2
Rephrased:
Example:
 Divide your paper in
half. On one side,
rephrase this standard
and on the other side,
provide an example.
 Share with your
partner.
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Alliance
Project
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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Alliance
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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 each
strata.
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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: won’t or can’t participate
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Errors of Observation
 Interview error- interaction between interviewer
and person being surveyed
 Respondent error: respondents have difficult time
answering the question
 Measurement error: inaccurate responses when
person doesn’t understand question or poorly
worded 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 of
each of the five rectangles.
Find the area of the five rectangles.
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Alliance
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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 the
actual area of all 100 rectangles.
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Alliance
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Practice
At 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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Alliance
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Practice
To conduct a survey of long-distance calling patterns, a researcher
opens a telephone book to a random page, closes his eyes, puts
his finger down on the page, and then reads off the next 50
names. Which of the following are true statements?
I. The survey design incorporates chance
II. The procedure results in a simple random sample
III. The procedure could easily result in selection bias
a)
b)
c)
d)
e)
I and II
I and III
II and III
I, II and III
None of the above gives the complete set of true responses
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Alliance
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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 2
children 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 teachers
were not selected randomly
b) No, because not all possible
groups of 30 children had the
same chance of being
chosen
c) No, because not all children
had the same chance of
being chosen
d) Yes, because each child had
the same chance of being
chosen
e) Yes, because the numbers
were assigned randomly to
the 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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