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Anticipate patterns and variations variable intuition graph-sense88 %ISTATISTICS SAY& Students heights would show more variability than guesses of my age KDC Pursues High-Return, Low-Risk Strategyr8What is Variability?  s9What is Variability?  t:Describing VariabilityzThe  bumpiness of a histogram does not determine the variability of the observations The number of distinct values the variable takes does not determine the variability of the observations66 ] v;STATISTICS SAY& 5236 drivers age 65 and over were involved in fatal accidents, compared to only 2900 drivers aged 16 and 17, so young people are safer drivers... 65% of motorcycle fatalities occurred in states with mandatory helmet laws...w<Counts Versus Ratios6Simple counts are often not a good basis for comparison of two or more groups. Group size isn t always obvious two groups of 25 U.S. states may have very different sizes even though both include the same number of states. Deciding on a sensible basis for comparison requires thought!ZJSTATISTICS SAY& }85% of software developers predicted that Microsoft's integration of Internet functions into Windows would help their companySSome Simple Questions@Question 1 Lost ticket Yes: 6 No: 9 Lost $20 Yes: 8 No: 6: 4 (Some Simple QuestionsPeople are more likely to say  yes when they have lost a $20 bill People tend to answer  not surprising to both expressions People are more likely to choose program A with the  save version and program B with the  die versionSome Simple QuestionsBe careful when wording survey questions  ask to see the phrasing! Bill Gates: It would help me EMENSELY to have a survey showing that 90% of developers believe putting the browser into the operating system is a good idea& Browser vs.  browser technologies &##  STATISTICS SAY & Researchers in Philadelphia investigated whether pamphlets containing information for cancer patients are written at a level that the cancer patients can comprehend Median reading levels are equal B  !Readability of Cancer Pamphlets  "Readability of Cancer PamphletsAGraphs can illuminate Look at the data! Think about the question8A#STATISTICS SAY& iAmerican men were randomly selected for the 1970 draft Draft numbers (1-366) were assigned to birthdates ^ Q Draft Lottery~Calculate the median draft number for each month 31 days: 16th value 30 days: average 15th and 16th values 29 days: 15th value1N % Draft Lottery [month median January 211.0 February 210.0 March 256.0 April 225.0 May 226.0 June 207.5 \[ [ fmonth median July 188.0 August 145.0 September 168 October 201 November 131.5 December 100gg & Draft Lottery   ' Draft Lottery   ( Draft Lottery IStatistics matter Summaries can illuminate Randomization can be difficultISTATISTICS SAY& ZThe average time between eruptions of the Old Faithful Geyser is 71 minutes August, 1985 BL L Geyser Eruptions   Geyser EruptionsVLooks can be deceiving! Use the graph that summarizes without losing important detailsKSTATISTICS SAY& SThe average major league baseball salary in the United States is about $1.5 million Rowers WeightsF2000 Men s Olympic Rowing Team 2" Rowers Weights   Rowers Weights Mean Median Full Data Set 197.29 207.5 Without Coxswain 200.11 210.00 Without Coxswain or 210.57 210.00 lightweight rowers With heaviest at 320 215.33 210.00 Resistance....,Rowers Weights|Know what your numerical summary is measuring Investigate causes for unusual observations Baseball: median salary ~ $500,000.STATISTICS SAY&   0Televisions and Life Expectancy4Buy another television? Association is not causationY&STATISTICS SAY& jOverall survival rates: A: 80% B: 90% Fair condition: A: 98.3% B: 96.7% Poor condition: A: 52.5% B: 30.0%t Z'Hospital Recovery Rates Simpson s Paradox Hospital A gets most of the poor condition cases Patients in poor condition are less likely to survive Thus: hospital A has the lower survival rate despite being the better choice for either condition Beware of lurking variables6[(Hospital Recovery Rates (cont.)  \)Hospital Recovery Rates (cont.)  ]*Hospital Recovery Rates (cont.)  LSTATISTICS SAY& ZTaking an aspirin each day reduces the risk of heart attack for men, but less so for women=-How Experiments Take Variability Into Account( Direct control Blocking Randomization> Randomization  ?Blocking Scheme A  @Blocking Scheme B  AResults from 100 Trials  BControlling for VariabilityBlocking reduces variability in the estimated mean difference Homogeneous blocks are desirable Randomization evens out the effects of extraneous variablesMSTATISTICS SAY& :A log was selected at random& C Sampling LogsDoes choosing times at random result in a random sample of logs? _______________________________ 8C'h((DEstimating Mean String LengthDoes the sampling procedure produce a simple random sample? How is this related to the log problem?? Can you suggest a better sampling method?m6Selecting a SampleRandom Sampling eliminates human selection bias so the sample will be fair and unbiased/representative of the population. 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