#3 Modules 2-2 and 2-3

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Apr 3, 2024

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Modules 2-2 and 2-3: Chapters 3 and 4 Question 1: After years of grade inflation, students’ grades are generally uni-modal and skewed to the left. In this case, we expect: (a) Mean > median > mode (b) Median > mean > mode (c) Mode > median > mean (d) Mean > mode > median (e) Mode > mean > median

Question 2: The following box-plot is for wealth of the world's 100 richest people in 2007 (in billions of dollars). Which one of the following statements is TRUE? (a) The corresponding histogram will be left-skewed. (b) More than 50% of the data is between 10 and 15 million dollars. (c) The mean has a higher value than the median. (d) The standard deviation is 100 million dollars. (e) The standard deviation and IQR are equal.

Question 3: The following given is the information on a data set of 24 points. Min Q1 Q2 Q3 Max 11.0 16.0 17.5 19.0 23.0 Based on the 1.5 IQR-rule, which of the following statement is TRUE? (a) There are no outliers in this data. (b) 23.0 is an outlier. (c) 11.0 is an outlier. (d) Both 11.0 and 23.0 are outliers. (e) There isn’t sufficient information to determine the outliers.

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Question 4: The following stem-and-leaf display shows populations of 50 states and Washington, DC, in millions of people, according to the 2000 census. 3 | 4 2 | 2 | 1 1 | 69 1 | 0122 0 | 5555666667888 0 | 11111111111112222233333334444 State Population (1|2 means 12 million) Based on the stem-and-plot diagram, which of the following conclusion about the distribution of the data is TRUE ? (a) Skewed to the right, (b) Skewed to the left, (c) Symmetric, (d) Symmetric with one outlier, (e) Neither skewed to the right nor to the left.

Question 5: Twenty-five students were selected from three classes, A, B, and C. The following is the histogram of their marks. Which of the following is true about the mean and/or median of the three groups? (a) median(A) > median(B) > median(C) (b) median(B) > median(A) > median(C) (c) median(C) > median(B) > median(A) (d) median(A) < mean(A) (e) Mean(C) > mean(B) > mean(A)

Question 6: Consider the following data: 90 93 99 76 84 85 86 86 100 91 80 82 What are median and IQR of the data? (a) Median = 85.5 and IQR = 8.0 (b) Median = 85.5 and IQR = 9.0 (c) Median = 86.0 and IQR = 8.0 (d) Median = 86.0 and IQR = 9.0 (e) Median = 86.5 and IQR = 8.0

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Question 7: The following set of observations has a sample variance of 6. {2, 3, 4, 5, 6, 7, 8, 9} Which of the following statements is TRUE ? (a) The sample variance of {2, 3, 4, 5} is 6. (b) The sample variance of {2, 4, 6, 8} is 6. (c) The sample variance of {1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5} is more than 6. (d) The sample variance of {2, 3, 4, 5, 6, 7, 8, 9, 10} is less than 6. (e) The sample variance of {3, 4, 5, 6, 7, 8, 9, 10} is 6.

Question 8: If the distribution of body temperatures has a mean of 37 °C with a standard deviation of 0.35 °c, then what are these values when converted to °F? ( Hint: To convert °C to °F, we use 1.8 32 O O F C   ) (a) Mean = 98.6 and Standard deviation = 0.63 (b) Mean = 98.6 and Standard deviation = 32.63 (c) Mean = 66.6 and Standard deviation = 0.63 (d) Mean = 66.6 and Standard deviation = 32.63 (e) Mean = 82.6 and Standard deviation = 16.63

Question 9: The mean and standard deviation for the long jump and 200m in the 2008 Olympics (when measured in meters) are given in the following table: Long Jump 200m 6.11 x  24.71 y  0.238 x s  0.7 x s  Nataliya Dobrynska of the Ukraine posted a long jump of 6.63 meters and ran the 200m in 23.21 seconds. Which was a more impressive feat? (a) Her performance was more impressive in long jump. (b) Her performance was more impressive in 200m. (c) Her performance was the same in both long jump and 200m. (d) We cannot compare her performance since they belong to different sport groups. (e) We can compare her performances if more information is provided.

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Quiz 10: Here are the summary statistics of the basketball team’s score per game for last year: mean = 58 points, standard deviation = 9 points. Suppose the opponents' score was 10% lower. Find the opponents' mean and standard deviation. (a) Mean = 52.2 points, SD = 8.1 points (b) Mean = 52.2 points, SD = 9 points (c) Mean = 63.8 points, SD = 9.9 points (d) Mean = 52.2 points, SD = 0.9 points (e) Mean = 52.2 points, SD = 8.9 points

Quiz 11: Mrs. Clark belongs to an age group for which the mean weight is 112 pounds with a standard deviation of 11 pounds, and Mr. Clark, her husband, belongs to an age group for which the mean weight is 163 pounds with a standard deviation of 18 pounds. If Mrs. Clark weighs 132 pounds and Mr. Clark weighs 183 pounds, which of the following statements is TRUE? (a) Relative to their age groups, Mrs. Clark somewhat weighs more than Mr. Clark. (b) Relative to their age groups, Mr. Clark somewhat weighs more than Mrs. Clark. (c) Relative to their age groups, neither Mrs. Clark nor Mr. Clark weighs more since both are 20 pounds above their group average. (d) Relative to their age groups, we cannot compare Mrs. and Mr. Clark since they belong to different age groups. (e) Relative to their age groups, we can compare Mrs. and Mr. Clark if more information is provided.