Sampling s3 12-01-17-2012


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Sampling s3 12-01-17-2012

  1. 1. Information fromSamplesAlliance ClassJanuary 17, 2012MathAllianceProject
  2. 2. AgendaLessons for StudentPostersCCSS Grade 7 StatisticsTypes of SamplingSampling ActivitiesMathAllianceProject
  3. 3. Lesson Plans for Student PostersDay 1: Brainstorming 2/17Day 2: Sort and Classify Questions 2/17Day 3: Planning 2/17Day 4: Data Collecting 3/17Day 5: Graphs 3/17Day 6: Poster 4/1 or spring breakMathAllianceProject
  4. 4. WALT1. Develop an understanding of 7.SP.1 and 2.2. Understand the different methods of collecting asample from a population.3. Understand the need for random selection of asample.MathAllianceProject
  5. 5. Success Criteria When I am able to clearly explain and provide anexample for CCSS standard 7.SP. 1and 2. When I am able to identify the different methods ofsampling and explain why random sampling isimportant.MathAllianceProject
  6. 6. CCSS 7th Grade StatisticsDomainUse 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.MathAllianceProject
  7. 7. CCSS Grade 7 Statistics Domain2. 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 byrandomly sampling words from the book;predict the winner of a school election basedon randomly sampled survey data. Gaugehow far off the estimate or prediction mightbe.MathAllianceProject
  8. 8. Standard 7.SP.1 Read Standard 7.SP.1 Divide your paper inhalf. On one side,rephrase this standardand on the other side,provide an example. Share with yourpartner.Standard 7.SP.1Rephrased: Example:MathAllianceProject
  9. 9. Standard 7.SP.2 Read standard 7.SP.2 Divide your paper inhalf. On one side,rephrase this standardand on the other side,provide an example. Share with yourpartner. MathAllianceProjectStandard 7.SP.2Rephrased: Example:
  10. 10. Types of Sampling Simple Random Sample Stratified Random Sample Cluster sampling Systematic ConvenienceMathAllianceProject
  11. 11. Simple Random Sample Every subset of a specified size n from thepopulation has an equal chance of being selectedMathAllianceProject
  12. 12. Stratified Random Sample The population is divided into two or more groupscalled strata, according to some criterion, such asgeographic location, grade level, age, or income,and subsamples are randomly selected from eachstrata.MathAllianceProject
  13. 13. Cluster Sample The population is divided into subgroups (clusters)like families. A simple random sample is taken ofthe subgroups and then all members of the clusterselected are surveyed.MathAllianceProject
  14. 14. Systematic Sample Every kth member ( for example: every 10thperson) is selected from a list of all populationmembers.MathAllianceProject
  15. 15. Convenience Sample Selection of whichever individuals are easiest toreach It is done at the “convenience” of the researcherMathAllianceProject
  16. 16. Errors in Sampling Non-Observation Errors Sampling error: naturally occurs Coverage error: people sampled do not match thepopulation of interest Underrepresentation Non-response: won’t or can’t participateMathAllianceProject
  17. 17. Errors of Observation Interview error- interaction between interviewerand person being surveyed Respondent error: respondents have difficult timeanswering the question Measurement error: inaccurate responses whenperson doesn’t understand question or poorlyworded question Errors in data collectionMathAllianceProject
  18. 18. Random Rectangles1. When given the cue turn the paper over.Within 5 seconds make a guess for theaverage area of the rectangles.2. When given the cue turn the paper over.Select 5 rectangles you think arerepresentative of the rectangles on the page.Write the rectangle numbers and their areas.Compute the average of the 5 rectangles.MathAllianceProject
  19. 19. Random Rectangles3. Use the random-number generator on thegraphing calculator to select five differentnumbers from 1 to 100.Write down the five numbers and the area ofeach of the five rectangles.Find the area of the five rectangles.MathAllianceProject
  20. 20. Random RectanglesReport the three answers that you found for theaverage of the rectangles.1.Guess2. Representative sample3.Random sampleAt your table construct 3 box plotsMathAllianceProject
  21. 21. Random RectanglesCompare the three box plots. Describe anysimilarities and differences.Compare the medians of the three box plots to theactual area of all 100 rectangles.MathAllianceProject
  22. 22. PracticeAt your table explain how you would conduct:• A simple random sample of teachers in our class• A stratified random sample of teachers in ourclass• A systematic sample of teachers in our classMathAllianceProject
  23. 23. PracticeTo 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 chanceII. The procedure results in a simple random sampleIII. The procedure could easily result in selection biasa) I and IIb) I and IIIc) II and IIId) I, II and IIIe) None of the above gives the complete set of true responsesMathAllianceProject
  24. 24. PracticeA large elementary school has 15classrooms, with 24 children in eachclassroom. A sample of 30 children ischosen by the following procedure:Each of the 15 teachers selects 2children from his or her classroom tobe in the sample by numbering thechildren from 1 to 24, using a randomdigit table to select two differentrandom numbers between 01 and 24.The 2 children with those numbers arein the sample.Did this procedure give a simple randomsample of 30 children from theelementary school?a) No, because the teacherswere not selected randomlyb) No, because not all possiblegroups of 30 children had thesame chance of beingchosenc) No, because not all childrenhad the same chance ofbeing chosend) Yes, because each child hadthe same chance of beingchosene) Yes, because the numberswere assigned randomly tothe childrenMathAllianceProject
  25. 25. Visual Bias Pull the slide until the line on the slide looks as if itis the same length as the line on the face of thecard. Turn the card over and read the length Record this length and report it when asked.MathAllianceProject
  26. 26. 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? Dothey appear to be systematically too long or tooshort?MathAllianceProject
  27. 27. 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 asthe spinner to generate the random numbers thatare needed for A1 and 2.MathAllianceProject