Calculating Variance and Standard Deviation: Data Exam Insights

Distributions of Data Exam 100% 1. Using the test scores in the table below, what is the variance of the scores on the exam? (Round your answer to the nearest whole number.) 18 21 24 27 31 2. Using the test scores in the table below, what is the standard deviation of the scores on the exam? (Round your answer to the nearest whole number.) 3 5 6 7 9 Explanation:

Determine that the average score is 87% Calculate all of the differences between the scores and the average to get 9, 5, 4, 3, 0, - 1, -1, -4, -5, -10 Square all of the differences to get 81, 25, 16, 9, 0, 1, 1, 16, 25, 100 Average the squared differences to get 27.4 as the variance Take the square root of the variance to get 5.23 as the standard deviation Round 5.23 to the nearest whole number to get 5 Answer: 5 3. Assume that 500,000 people take the GED exam (high school proficiency exam) each year and their scores form a normal distribution. If Danny scores two standard deviations below the mean, what percentile is he? 2.5th 5.0th 12.5th 22.5th Not enough information to determine. 4. Assume that 500,000 people take the GED exam (high school proficiency exam) each year and their scores form a normal distribution. If Tara scores one standard deviation above the mean, what percentile is she? 34th 68th 84th 95th Not enough information to determine. 5. Assume that 20 people take a math test, which is not enough for a normal distribution to form. If Conrad scores three standard deviations above the mean, what percentile is he? 75.0th 88.5th 95.0th 99.7th Not enough information to determine. 6.

Assume that 20 people take a math test, which is not enough for a normal distribution to form. If Sarah scores at the median, what percentile is she? 34th 50th 68th 95th Not enough information to determine. 7. Assume that 20 people take a math test, which is not enough for a normal distribution to form. If Charlie scores at the mean, what percentile is he? 44th 50th 56th 68th Not enough information to determine. 8. Compare the times of the two marathons runners in the table below. Which marathon runner is more likely to win the marathon on any given day? Runner 1 Runner 2 They have the same likelihood of winning. They have a different likelihood, but it cannot be determined who is more likely. Not enough information to determine. 9. Compare the times of the two marathons runners in the table below. Which marathon runner has a higher variance in her performance?

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Runner 1 Runner 2 They have the same variance. They have a different variance, but it cannot be determined who has a higher variance. Not enough information to determine. 10. Typically, in the early stages of a country's transition from an emerging nation to a developed nation, death rates fall while birth rates stay constant. What type of covariance do death rates and birth rates have? Positive Covariance Negative Covariance No Covariance Inverse Covariance Not enough information to determine. 11. Typically, in the middle stages of a country's transition from an emerging nation to a developed nation, death rates fall while birth rates fall. What type of covariance do death rates and birth rates have? Positive Covariance Negative Covariance No Covariance Inverse Covariance Not enough information to determine. 12. Typically, in the late stages of a country's transition from an emerging nation to a developed nation, death rates stay constant while birth rates fall. What type of covariance do death rates and birth rates have? Positive Covariance Negative Covariance No Covariance Inverse Covariance Not enough information to determine.

13. If a company’s profits increase when the economy slows, what type of covariance is there between this company and the broader economy? Positive Covariance Negative Covariance No Covariance Inverse Covariance Not enough information to determine. 14. If the average height of a male in the U.S. is 70 inches and the standard deviation of male heights is 3 inches, what is the probability that a randomly selected male will be between 70 and 73 inches? (Assume a normal distribution.) 18% 34% 50% 68% Not enough information to determine. 15. If the average height of a female in the U.S. is 65 inches and the standard deviation of female heights is 2.5 inches, what is the probability that a randomly selected female will be between 60 and 62.5 inches? (Assume a normal distribution.) 5% 14% 18% 24% Not enough information to determine.

Distributions of Data Exam Wk 5

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