1. From Data to Decision: Refer to the indicated data set in Table 2-1. A. Refer to the indicated Table 2-1 data set - Explain your findings 1. Identify the class width, class midpoints, and class boundaries for the given frequency distribution. For these data sets, it seemed appropriate to use a class width of 5 years, starting with age 20. Under these conditions, the class midpoints are: 22.5, 27.5, 32.5, 37.5, 42.5, 47.5, 52.5, 57.5, 62.5, 67.5, 72.5, 77.5, 82.5. The class boundaries are: 19.5, 24.5, 29.5, 34.5, 39.5, 44.5, 49.5, 54.5, 59.5, 64.5, 69.5, 74.5, 79.5, 84.5 2. Construct a Relative Frequency Table Age Best Actress (Count) Best Actress (%) Best Actor (Count) Best Actor (%) 20-24 4 5.3% 0 0% 25-29 22 29.0% 1 1.3% 30-34 15 19.7% 9 11.8% 35-39 16 21.1% 15 19.7% 40-44 9 11.8% 22 28.9% 45-49 3 3.9% 11 14.5% 50-54 2 2.6% 8 10.5% 55-59 0 0% 4 5.3% 60-64 3 3.9% 5 6.6% 65-69 0 0% 0 0% 70-74 1 1.3% 0 0% 75-79 0 0% 1 1.3% 80-84 1 1.3% 0 0% 1 Construct a Cumulative Frequency Distribution Table Age Best Actress (Count) Best Actress (%) Best Actor (Count) Best Actor (%) Less than 25 4 5.3% 0 0% Less than 30 26 34.2% 1 1.3% Less than 35 41 53.9% 10 13.2% Less than 40 57 75% 25 32.9% Less than 45 66 86.8% 47 61.8% Less than 50 69 90.8% 58 76.3% Less than 55 71 93.4% 66 86.8% Less than 60 71 93.4% 70 92.1% Less than 65 74 97.4% 75 98.7% Less than 70 74 97.4% 75 98.7% Less than 75 75 98.7% 75 98.7% Less than 80 75 98.7% 76 100% Less than 85 76 100% 76 100% B. Construct and determine the value of each measure of center and interpret those values. Best Actress (age in years) Best Actor (age in years) Mean (sum of all ages divided by total number of people) 35.6 43.9 Median (middle age, chronologically) 33.5 42 Mode (most common age) 35 41 and 42 Midrange ((max age + min age)/2) 50.5 52.5 Each of the measures of center is less for Actresses than Actors. This means that in general, Best Actress winners tend to be younger than Best Actor winners. C. Construct and determine the values of measure of variation and interpret those values. Best Actress Best Actor Range (max age - min age) 59 yrs 47 yrs Variance 120.8 yr2 81.1 yr2 Standard Deviation 11.0 yrs 9.0 yrs Each of the measures of variation is greater for Actresses than Actors. This means that over the years, there has been greater variety in the ages of Best Actress winners than Best Actor winners. D. Construct Mean, Variance and Standard Deviation and interpret findings Best Actress Best Actor Mean 35.6 years old 43.9 years old Variance 120.8 yr2 81.1 yr2 Standard Deviation 11.0 yrs 9.0 yrs Based on the histograms, the data are somewhat normally distributed, although they also appear to be skewed slightly right. Using the range rule of thumb, which states that for many data sets, the vast majority (95%) of the data points should lie within 2 standard deviations of the mean, we can interpret these results to mean that: The vast majority (95%) of Best Actresses are between 13.6 and 57.6 years old. The vast majority (95%) of Best Actors are between 25.9 and 61.9 years old. If the data were normally distributed, we could use the empirical rule to also say that: 68% of Best Actresses are within 1 standard deviation of the mean, between 24.6 and 46.6 years old. 95% of Best Actresses are within 2 standard deviations of the mean, between 13.6 and 57.6 years old. 99.7% of Best Actresses are within 3 standard deviations of the mean, between 2.6 and 68.6 years old. 68% of Best Actors are within 1 standard deviation of the mean, between 34.9 and 52.9 years old. 95% of Best Actors are within 2 standard deviations of the mean, between 25.9 and 61.9 years old. 99.7% of Best Actors are within 3 standard deviations of the mean, between 16.9 and 70.9 years old. E. Critical Thinking: Address the following questions 1. Are there differences between the ages of the Best Actresses and the ages of the Best Actors? 2. Does it appear that actresses and actors are judged strictly on the basis of their artistic abilities? 3. Does there appear to be discrimination on age, with the Best Actresses tending to be younger than the Best Actors? Are there any other notable differences