Statistical Data Exploration
Activity 4.1 Data ExplorationIntroductionThe understanding and manipulation of data allows decision making to be based on outcomes and even predictions. Statistical calculations can be theory-based. Calculations can also be established through manipulation of data collection or experimentation. To better understand the advantages and limitations of both processes of probability, statisticians must have understanding and experience working with both theory and experimental data. EquipmentCoinDice or digital diceCalculatorProcedureWhat is the probability that the illustrated board game spinner will land on blue?Define the ExperimentThe Arrow spins with an equal chance ofLanding on one of the colorsDefine the Sample SpaceThe sample space is one of the 6 possible spaces. Each space has the same areaDefine the EventArrow spins, lands on space.Solve for Probability0.1666666666666667What is the probability of a flipped coin landing on heads?50%What is the probability of a flipped coin landing on heads 4 times out of 6 trials?Calculate the probability of a flipped coin landing on heads through experimentation.Toss a fair coin 10 times and record your data below.TossHeadsTails112131415161718191101Total 46Calculate the relative frequency of the coin landing on heads after 10 trials.40%60%Toss a fair coin 50 times and record your data below.TossHeadsTails112131415161718191101111121131141151161171181191201211221231241251261271281291301311321331341351361371381391401411421431441451461471481491501Total 2426Calculate the relative frequency of the coin landing on heads after 50 trials.48 % or 0.48Collect the relative frequency data from your entire class and determine the relative frequency of the coin landing on heads.Describe the relationship between the relative frequency of the coin landing on heads and the probability of a single coin landing on heads. Does sample size affect this relationship? Create a histogram representing the summation possibilities of rolling two dice simultaneously (Note: rolling a 2 and a 3 is not the same as rolling a 3 and a 2).SumEventFrequency21-131-2, 2-141-3, 3-1, 2-251-4, 2-3., 3-2, 4-161-5,2-4,3-3,4-2,5-171-6,2-5,3-4,4-3, 5-2, 6-186-2, 2-6, 5-3, 3-5, 4-495-4, 4-5, 6-3, 3-6, 105-5, 6-4, 4-6116-5, 5-6, 126-6What is the probability of rolling a 7?0.0833333333333333 8%What is the probability of rolling a 12?0.0833333333333333 8%What is the probability of not rolling a 9? 0.9166666666666667 92% Simultaneously roll two dice 50 times and record your data below.Die #1Die #2Trial123456123456Total11182116311541155111061167116811891121011611114121171311121411101511616117171161811519116201142111922117231192411525115261192711728117291133011113111432114331112341143511736111237117381111391194011741115421184311644119451134611747114481144911750119Total 81112103669115910112What is the relative frequency of rolling a summation of 7?0What is the relative frequency of rolling a summation of 12?1/12What is the relative frequency of rolling a 6 on a single die?1/6What is the relative frequency of rolling a summation of 6?2/12Were your dice loaded? Justify your answer.ConclusionOne coin is flipped four times. What is the probability of flipping two heads and two tails? A set of two die are rolled twice. What is the probability of rolling “snake eyes” on both rolls? A sunglasses manufacturer receives frames from three manufacturing companies. What is the probability that a defective frame was manufactured by company three?FactoryPercent of ProductionProbability of Defect162%.020230%.01338%.027 ................
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