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Grade 9 Statistics and Probability ResourceProbability can be written as a fraction, decimal, or percent. For example, a 30% probability ofrain could be written as 3/10 or 0.3All probability values lie between zero (likelihood it will never occur) and one (likelihood it willalways occur) inclusive (or between 0% and 100%).Think about the following events. How likely is each to occur? (assign a number between 0 and1 for each event).a)b)c)d)The sun will rise tomorrow.It will snow in the middle of July in Regina.A new student in our class will be a girl.You will pass Math 90.Experimental probability is the probability which results from a given experiment or pastexperience.i.e. The weather forecast says there is a 70% chance of snow.Theoretical probability is the result based upon mathematically deriving it from all the givenequally favorable outcomes.i.e. There is a 5 out of 26 chance that a randomly chosen letter is a vowel.Subjective judgment is the way you may strongly feel despite the given probability. Subjectivejudgments are decisions based on a “hunch” or a feeling.i.e. Buying a lottery ticket because you feel lucky todayWhat are some other examples?Experimental Probability Activities (i.e. flipping a coin, tossing a die)14November 2015 GSCS

Grade 9 Statistics and Probability ResourceTheoretical Probability Examples:1)What is the probability of rolling a six on a six sided die?2)What is the probability of picking a queen out of a normal deck of cards?3)What is the probability of tossing a head on a normal quarter?4)What is the probability of rolling a number greater than 2 on a normal six sided die?Read over examples 1 – 3 on pages 425 – 427Assignment: Pages 427 - 429, # 1 – 11, 17Assessment Focus #11, Reflect (in journal)Math Link p. 429 – discuss in class15November 2015 GSCS

Grade 9 Statistics and Probability ResourceGame: Cube Master p. 430CubeColorsInitialGuessGuess afterGuess after10 cubes20 cubesGuess after 30cubesActual # ofcubes# ofpointsBlueGreenBlack16November 2015 GSCS

Grade 9 Statistics and Probability Resource9.2 Potential Problems with Collecting DataDo “investigate” on Page 431 in groups of 4.Below are several factors that could affect data collection. Please provide your own examplefor each.PotentialProblem:What it means:BiasThe question influences responses in favourof, or against the topic.Use oflanguageThe use of language in a question could leadpeople to a particular answer.TimingWhen the data is collected could lead toparticular results.PrivacyIf the topic of the data collection is personal,a person may not want to participate or maygive an untrue answer. Anonymous surveysmay help.CulturalSensitivityThis means that you are aware of othercultures. You must avoid asking questionsthat may be offense to some cultures.EthicsData collected must not be used for thepurposes other than those communicated tothe participants.CostThe cost of collecting data must be taken intoaccount.TimeThe time needed for collecting the data mustbe considered.Your own example:Going back to “investigate”, identify which potential problems could be related to eachquestion.17November 2015 GSCS

Grade 9 Statistics and Probability ResourceRead the examples on Page 433 - 434Assignment: Pages 435 - 436, # 1 – 16Assessment Focus #13, Reflect (in journal)18November 2015 GSCS

Grade 9 Statistics and Probability Resource9.3 Using Samples and Populations to Collect DataInvestigate p. 43710 fish sample#%20 fish sample#%40 fish sample#%Actual Population#%malefemaleHow did your percents compare with the actual percents? In general, how did your estimateschange as the size of the sample increased?Population – is the group about which you are getting information.Census – is a tool used to collect data from every member of the population. This can be timeconsuming, costly and difficult (if not impossible) to x-eng.cfmSample – is a small portion of the populationValid conclusions – when the sample chosen is representative of the populationRead examples on Page 438 - 440Assignment: Pages 440 – 441, # 1 – 13Assessment Focus #10, Reflect (in journal)Mid-Unit Review: Page 444, # 1 – 9 all19November 2015 GSCS

Grade 9 Statistics and Probability Resource9.4 Selecting a SampleInvestigate p. 445Define each of the following types of sampling in your own words and provide an example (seepage 446):Simple random samplingSystematic/interval samplingCluster samplingSelf-selected samplingConvenience samplingStratified random samplingNow go back to “investigate” and try to classify the different methods of sampling using theterminology above.Read Examples on Page 447Assignment: Pages 447 - 449, #1 - 12Assessment Focus # 8, Reflect (in journal)20November 2015 GSCS

Grade 9 Statistics and Probability ResourceTypes of Sampling:1.Simple random – each member of the population has an equal chance of beingselectedEx.2.Systematic or interval sampling – every nth member is selectedEx.3.Cluster sampling – every member of each randomly chosen group of thepopulation is selected.Ex.4.Self-selected sampling – only members who are interested and volunteer willparticipate.Ex.5.Convenience sampling – only members of the population who are convenientto include are selected.Ex.6.Stratified random sampling – some members from each group of thepopulation are randomly selected.Ex.21November 2015 GSCS

Grade 9 Statistics and Probability Resource9.5 Designing a Project Plan(This may be used as an option when students are assigned the Data Collection Project for OutcomeSP9.2)Investigate p. 454Read through the Connect on p. 454Did your plan from “investigate” contain all these steps?Discuss the example on page 455Day 1 – Project Plan:Go through project evaluation rubric with students (Teachers - see Master 9.3 on p. 53 ofProGuide)Have students read pages 454 - 455 and do Questions # 1 – 10 on page 455 - 456Students Collect DataDay 2 - Unit Problem: Students work through activities and Questions on Page 461.Your project is due on .You must hand-in the following: The project plan from Section 9.5 (Questions 1-10) The display of your data (chart and graph) and your conclusions Answers to the presentation questions on Page 461 Your rubric and self-assessmentUnit Review: Pages 458 – 459, #1 – 16Due:22November 2015 GSCS

Grade 9 Statistics and Probability ResourceStatistics and Probability Assessment (Outcomes SP9.1 & SP9.3)(Source: Math Makes Sense Unit 9 Test)Name:Outcome: SP9.1Demonstrate understanding of the effect of bias, use of language, ethics, cost, timing,privacy, cultural sensitivity, population or sample on data collection.Outcome: SP9.3Demonstrate an understanding of the role of probability in society.1. A die with 6 faces is rolled 10 times. Each time, the die shows an even number.Klaus predicts the next roll will be odd.Joanna predicts the next roll will be even.Nicholas predicts the next roll is equally likely to be even or odd.Which type of probability might each person have made his or her prediction? (Theoretical,experimental or subjective judgement)2. Jenna thinks she is likely to score a goal in tonight’s soccer game since she has scored a goalin 4 of her last 5 games.a) What assumptions is Jenna making?23November 2015 GSCS

Grade 9 Statistics and Probability Resource3. Identify a potential problem with each data collection. Justify your answer.a) Rachel asks: “What costume will you wear for Halloween this year?”b) Jerome asks local dog kennels: “How often do you walk the dogs in your care?”c) A dentist sends a questionnaire to her patients 6 months after their last check-up, askingthem to rate the quality of care they received and reminding them to make an appointmentfor a new check-up.4. Would you use a census or a sample to gather each set of data? Justify your choice.a) To determine whether the strings of a guitar are in tune24November 2015 GSCS

Grade 9 Statistics and Probability Resourceb) To determine citizens’ opinions about the new traffic lawsc) To test the quality of a new recipe for a cookbook5. What sampling method is used in each situation? Will it give valid conclusions? Justify youranswers.a) A radio show invites city residents to call in their opinions about the city’s crime rate.b) To predict which movie will win a People’s Choice Award, Carlos asks his friends whichmovies were their favourites.c) For a week, every 10th customer leaving a restaurant is asked to rate the food and theservice.6. Adriane mails a questionnaire asking, “Do you think there is a litter problem in ourneighbourhood?” to every house on her street. What problems might Ariadne encounter as shecollects data? Describe the effect each problem would have on her results.25November 2015 GSCS

Grade 9 Statistics and Probability ResourceSupplementary Question Bank for ath%20Study%20Guide%20(76%20pages).pdf)1. Describe the effect of: bias use of language ethics cost time and timing privacy cultural sensitivity on the collection of data. QUESTION 1Analyze a given case study of data collection; and identify potential problems related to bias, useof language, ethics, cost, time and timing, privacy or cultural sensitivity.SolutionB (timing)Surveying about a ice rink (typically a winter sport) in the summer.QUESTION 2SolutionB (cultural sensitivity)Individual beliefs is a factor to consider26November 2015 GSCS

Grade 9 Statistics and Probability Resource Provide examples to illustrate how bias, use of language, ethics, cost, time and timing, privacy orcultural sensitivity may influence data.QUESTION 3QUESTION 4QUESTION 5QUESTION 627November 2015 GSCS

Grade 9 Statistics and Probability Resource2. Select and defend the choice of using either a population or a sample of a population to answer aquestion. Identify whether a given situation represents the use of a sample or a population.Simple Random Sampling – this type of sampling involves each member of the population having anequal chance of being selected.Systematic or Interval Sampling – this sampling involves starting randomly and then selecting everynth member from then onwardsCluster Sampling - total population is divided into groups or clusters and every member of therandomly selected group is chosen.Self-selected sampling – this sample only includes only members who are interested and volunteerto be part of a survey.Convenience Sampling – this can be known as grab or opportunity sampling. It involves the samplebeing selected from a population which is close to hand.Stratified Random Sampling – this includes randomly selecting members from each group of thepopulation.QUESTION 1QUESTION 228November 2015 GSCS

Grade 9 Statistics and Probability ResourceStatistics are numbers that describe data (the information that is collected to look at).We use statistics to make information more meaningful in everyday life and to understanddifferent trends (patterns) that we see. For example, Stats Canada uses the informationabout Canadian citizens to see rises and falls in immigration, births, deaths, etc.The information is not meaningful just as raw data (numbers that have not been looked at);it becomes meaningful and useful when it is analyzed.Before we can analyze data though, we need to collect it.Population – a collection of people you will get the information from when collecting dataCensus - is the procedure of obtaining and recording information about the members of agiven population. It is often done door-to-door.Sample – is a subset or small portion of the population from which the data is beingcollected from. The sample should be a good representation the entire population.Valid Conclusion – will result if the data is collected from a representative sample of thepopulationQUESTION 3QUESTION 429November 2015 GSCS

Grade 9 Statistics and Probability ResourceQUESTION 5QUESTION 6QUESTION 7 Provide an example of a situation in which a population may be used to answer aquestion, and justify the choice.QUESTION 1YES30November 2015 GSCS

Grade 9 Statistics and Probability ResourceQUESTION 2YES Provide an example of a question where a limitation precludes the use of apopulation; and describe the limitation, e.g., too costly, not enough time, limitedresources.QUESTION 1Ava wants to determine what kind of pizza her friends on the volleyball team like the most. Which of the surveyingmethods would cost the most?A.Mailing out a questionnaire to all junior high studentsB.Telephoning a sample of 30 junior high studentsC.Asking the employees at a local pizza shop about the kind of pizza that is sold the mostD.Conducting personal interviews with a sample of 30 junior high students during recess Identify and critique a given example in which a generalization from a sample of apopulation may or may not be valid for the population.QUESTION 1QUESTION 231November 2015 GSCS

Grade 9 Statistics and Probability Resource Provide an example to demonstrate the significance of sample size in interpretingdata.QUESTION 1Which of the following samples is the best choice to see how many people see the eye-doctor for regularcheckups?A.25 people at the mallB.25 people who wear glassesC.25 people in the waiting room at the eye-doctorD.25 of your friendsQUESTION 2Outcome SP9.3 Demonstrate an understanding of the role of probability in society. Provide an example from print and electronic media, e.g., newspapers, the Internet, where probability isused.Did you ever wonder how the advertisers for Pepsi or Coke come up with their statistics? 8 out of every10 people choose Pepsi over Coke.Or have you ever wondered how they choose the “top 6 at 6:00” on Country 105 FM?We use statistics to make information more meaningful in everyday life and to understanddifferent trends (patterns) that we see. For example, Stats C

Grade 9 Statistics and Probability Resource 1 November 2015 GSCS . The intent of this document is to arrange all of the materials pertaining to the Statistics and Probability outcomes from the Saskatchewan Grade 9 M