1CRE: Oscar Winners - Listed below are the differences (in years) between the ages of actresses and actors when they won Oscars. The differences are found by subtracting the age of the male winner from the age of the female winner: (actress age) — (actor age). The differences are found using results from the last 12 years (as listed in Data Set 11 in Appendix B). ?20 ?15 ?3 ?12 6 ?15 ?7 ?9 16 ?18 ?15 ?15 a. Find the mean. Compare the result to the value of the mean that would be expected if there is no gender discrepancy between the ages of Oscar-winning actresses and actors. b. Find the median. Compare the result to the value of the median that would be expected if there is no gender discrepancy between the ages of Oscar-winning actresses and actors. c. Find the standard deviation. d. Find the variance. Be sure to include the units of measurement. e. Find the value of the first quartile, Q1. f. Find the value of the third quartile, Q3. g. Construct a boxplot. What does the boxplot suggest about the distribution of the data?

Solution 1CRE: The goal is to answer questions (a), (b), (c), (d), (e), (f), (g). Step 1 of 7: (a) We are given the following 12 data points: -20, -15, -3, -12, 6, -15, -7, -9, 16, -18, -15, -15. Use the mean formula to calculate the sample mean of the data: x = i = 20 + (15) + (3) + (12) + 6 + (15) + (7) + (9) + 16 + (1=) 1071 8.9215) n 12 12 Therefore, the sample mean is approximately -8.92 years. If there is no age discrepancy, then the mean should be 0 years. Step 2 of 7: (b) We are given the following 12 data points: -20, -15, -3, -12, 6, -15, -7, -9, 16, -18, -15, -15. Order the number from smallest to largest: -20, -18, -15, -15, -15, -15, -12, -9, -7, -3, 6, 16 The median is the number in the middle. In this case, we have two “middle” numbers: -15 and -12. So, the median is the average of these two numbers: 15 + (12) median = 2 = 13.5 Therefore, the median is -13.5 years. If there is no age discrepancy, then the median should be 0 years. Step 3 of 7: (c) We are given the following 12 data points: -20, -15, -3, -12, 6, -15, -7, -9, 16, -18, -15, -15. In part (a), we found that the sample mean is x = 8.92. Use the sample standard deviation formula to find the standard deviation of the sample: 2 s = (ix x ) n 1 2 2 2 2 2 = (20 (8.92)) + (15 (8.92)) + (3 (8.92)) + ··· + (15 (8.92)) + (15 (8.92)) 12 1 = 124119168 = 113.1742545 10.64 Therefore, the standard deviation of the sample is approximately 10.64 years. Step 4 of 7: (d) In part (c), we found that the sample standard deviation is s = 10.64. By definition, the variance is the square of the standard deviation. So, the sample variance is: 2 2 s = (10.64) 113.2 2 Therefore, the sample variance is approximately 113.2 (years) .