Statistics - Cummulative Reviews - Quick Guides | Statistics

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Study GuideStatistics–Cummulative Reviews1.Quiz: Cumulative Review A1. QuestionIn the stem and leaf plot above 1|3 represents 13.Whatis the median for these data?Answer Choices• 29• 30.5• 32Correct Answer30.5Why This Is CorrectThemedianis the middle value when the data are arranged in order.Since the stem-and-leaf plot represents an ordered list of numbers, the median fallsHalfwaybetweenthe two middle values (because there is an even number of data points).Thataverage is30.5, so30.5 is the median.2.QuestionIn the stem and leaf plot above 1|3 represents 13.Whatis the inter‐quartile range for these data?Answer Choices• 8.5• 16.5• 36

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Study GuideCorrect Answer16.5Why This Is CorrectTheinterquartile range (IQR)measures the spread of the middle 50% of the data.It is found using:When the first quartile (Q1) and third quartile (Q3) are identified from the stem-and-leaf plot, thedifference comes out to16.5.3.QuestionFor the data set 2, 4, 5, 7, 8, 10, 12, 16,whatis the mean?Answer Choices• 7.111• 7.5• 8Correct Answer8Why This Is CorrectThemeanis the sum of all values divided by the number of values.Sum:There are8 numbers, so:

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Study Guide4.QuestionFor the data set 2, 4, 5, 7, 8, 10, 12, 16,whatis the variance?Answer Choices• 4.567• 6.5• 20.857Correct Answer20.857Why This Is CorrectVariance measures how spread out the data are from the mean.1.Mean=82.Find squared differences from the mean3.Add them and divide byn − 1(sample variance)The calculation gives approximately:So the correct variance is20.857.5.QuestionEach test in statistics class is worth 100 points. After four tests, a studentHasan average of 85.0.She scores 95.0 on the fifth test.Whatis her average for the five tests?

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Study GuideAnswer Choices• 87.0• 90.0• 93.0Correct Answer87.0Why This Is CorrectAverage after 4 tests is 85, so total points so far:Add the 5th test score:Now divide by 5 tests:6.QuestionWhatis the mean?Answer Choices• 13.5• 13.64• 14

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Study GuideCorrect Answer13.64Why This Is CorrectThemeanis found by dividing the total of all values by the number of values.Using the data from the given frequency table/graph, the calculated mean comes out to13.64.7.QuestionWhatis the relative frequency for time 15 seconds?Answer Choices• 0.08• 0.167• 0.24Correct Answer0.167Why This Is CorrectRelative frequency is:The frequency for15 secondscompared to the total gives:So the correct relative frequency is0.167.

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Study Guide8.QuestionA lottery uses three machines and each machineHas10 balls. In each machine, each ball is markedwith a different single digit from 0 to 9. One ball is randomly selected from each machine and thethree digit number is the winning number.Whatis the probabilitythatthe number is 123?Answer Choices• 1/1000• 1/729• 3/10Correct Answer1/1000Why This Is CorrectEach machineHas10 digits (0–9), so the probability of choosing a specific digit is:To get exactly123, you must get:•1 from machine 1•2 from machine 2•3 from machine 3Multiply:9.QuestionWhatis the probabilitythatthe student prefers hockey?

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Study GuideAnswer Choices• 1/2• 7/15• 8/15Correct Answer8/15Why This Is CorrectProbability is:From the given data,8 studentsprefer hockey out of15 total, so:10.QuestionWhatis the probabilitythatthe student is a female and prefers figure skating?Answer Choices• 1/4• 2/5• 2/3Correct Answer1/4Why This Is CorrectThis is ajoint probability(femaleandfigure skating):From the table,1/4of the students meet both conditions, so the probability is1/4.

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Study Guide11.QuestionWhatis the probabilitythatthe student is a male or prefers hockey?Answer Choices• 3/5• 3/4• 14/15Correct Answer14/15Why This Is CorrectThis is an“OR” probability, so we use:Using the counts from the table, the union (male or hockey) includes14 out of 15 students, so:12.QuestionWhatis the probabilitythatthe student prefers figure skating giventhatthe student is female?Answer Choices• 2/5• 2/3• 6/7

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Study GuideCorrect Answer2/3Why This Is CorrectThis is aconditional probability:From the data table,2/3 of the femalesprefer figure skating, so the probability is:13.QuestionA binomial experimentHas12 trials with probability of success 0.40 on each trial.Whatis the mean ofthe distribution?Answer Choices• 4.8• 5.0• 6.0Correct Answer4.8Why This Is CorrectFor a binomial distribution:Here, (n=12) and (p=0.40):

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Study Guide14.QuestionA binomial experimentHas12 trials with probability of success 0.40 on each trial.Whatis theprobability of exactly 4 successes?Answer Choices• 0.0420• 0.1208• 0.2128Correct Answer0.2128Why This Is CorrectUse the binomial probability formula:Evaluating the expression gives approximately:15.QuestionWhich of the following is an example of a parameter?Answer Choices• a population mean• a sample mean• a sample proportion

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