Information from Samples

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Information from Samples

• Alliance ClassJanuary 17, 2012

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AgendaLessons for Student PostersCCSS Grade 7
StatisticsTypes of SamplingSampling 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 break

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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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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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CCSS 7th Grade Statistics Domain

•  Use random sampling to draw inferences about a
  population.
• 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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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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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 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.

Standard 7.SP.2 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
  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 wont or cant 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 doesnt 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

• 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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Random Rectangles

• Report the three answers that you found for the
  average of the rectangles.
• Guess
• Representative sample
• 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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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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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) I and II
• b) I and III
• c) II and III
• d) 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 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.