Exam 3: Descriptive Measures

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A teacher records the test scores for the 30 students in her class. Corresponding to each score, she calculates a z-score. If you were the parents of a girl in the class, would you be more interested in knowing your daughter's test score or z-score? Explain your reasoning.

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The z-score is more useful as it indicates how the student did relative to the rest of the class. The test score is less useful since the parents do not know how difficult the test was. A score of 85 could be an excellent score on a difficult test or an average score on an easy test.

Find the median for the given sample data. -A new business had the following monthly net gains: \ 6205 \ 2234 \ 1466 \ 8930 \ 8640 \ 2204 \ 2263 \ 7749 \ 5245 \ 5642

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B

Solve the problem. -Here are 3 boxplots of weekly gas prices at a service station in the United States (price in $ per gallon). Compare the distribution of prices over the three years. Solve the problem. -Here are 3 boxplots of weekly gas prices at a service station in the United States (price in $ per gallon). Compare the distribution of prices over the three years.

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A

Determine the quartile or interquartile range as specified. -Determine the interquartile range. 2, 3, 6, 8, 9, 12, 2,

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Find the range for the given data set. -To get the best deal on a microwave oven, Jeremy called six appliance stores and asked the cost of a specific model. The prices he was quoted are listed below. \ 117 \ 511 \ 192 \ 616 \ 356 \ 313

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 Explain what each symbol represents: (i) Σ, (ii) n, (iii) xˉ\text { Explain what each symbol represents: (i) } \Sigma \text {, (ii) } n \text {, (iii) } \bar { x }

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A teacher records the test scores for the 30 students in her class. The standard deviation of the scores was 10. Corresponding to each score, she calculates a z-score. Hugh's test score was one and A half standard deviations below the mean. What would his z-score have been?

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Identify potential outliers, if any, for the given data. -The weights (in pounds)of 18 randomly selected adults are given below. 131 134 186 135 178 120 127 113 174 143 167 165 132 226 91 148 194 162

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Determine the quartile or interquartile range as specified. -The normal annual precipitation (in inches)is given below for 21 different U.S. cities. Find the third quartile, Q3.\mathrm { Q } _ { 3 } . 19.1 34.2 10.2 37.6 22.4 9.1 12.6 32.6 20.6 36.9 30.0 39.7 17.3 24.5 32.2 13.6 28.7 15.0 22.3 26.9 11.7

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Use the empirical rule to solve the problem. -At one college, GPA's have a roughly bell-shaped distribution with a mean of 2.9 and a standard deviation of 0.6. What percentage of students at the college have a GPA between 2.3 and 3.5?

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Construct and interpret a boxplot or a modified boxplot as specified. -The test scores of 40 students are listed below. Construct a boxplot for the data. 25 35 43 44 47 48 54 55 56 57 59 62 63 65 66 68 69 69 71 71 73 73 74 76 77 77 78 79 80 81 81 82 83 85 89 92 93 94 97 98

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Discuss the differences between the distributions represented by the two boxplots below. Assume the two boxplots have the same scale. Explain your reasoning. Discuss the differences between the distributions represented by the two boxplots below. Assume the two boxplots have the same scale. Explain your reasoning.

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Find the mode(s)for the given sample data. -Last year, nine employees of an electronics company retired. Their ages at retirement are listed below. Find the mode(s). 56 61 60 57 52 63 64 58 55

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Identify potential outliers, if any, for the given data. -The normal annual precipitation (in inches)is given below for 21 different U.S. cities. 32.4 30.3 34.6 65.6 22.1 31.8 16.6 28.0 36.2 59.4 25.5 47.2 45.6 8.3 27.4 18.9 13.0 31.4 24.2 11.8 35.4

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Find the median for the given sample data. -The distances traveled (in miles)to 7 different swim meets are given below: 20, 25, 40, 41, 63, 73, 88

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We want to compare two different groups of students, students taking Composition 1 in a traditional lecture format and students taking Composition 1 in a distance learning format. We know that the mean score on the research paper is 85 for both groups. What additional information would be provided by knowing the standard deviation?

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A variable x has a mean, µ, of 22 and a standard deviation, Ϭ, of 7. Determine the standardized version of x.

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The heights of the adults in one town have a mean of 66.8 inches and a standard deviation of 3.4 inches. What can you conclude from Chebyshev's rule about the percentage of adults in the town Whose heights are between 56.6 and 77 inches?

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Find the range for the given data set. -Rich Borne is currently taking Chemistry 101. On the five laboratory assignments for the quarter, he got the following scores. 21 35 20 48 58

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When finding the 5-number summary, it becomes easy to identify the outliers of a data set. Under what conditions should outliers be deleted, and when should they be further investigated?

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