Measures of Variability Skewness and Kurtosis

Exercise 5.2 1. Convert the following real scores into standard scores. Given: x = 9.25 and s = 2.14 a. X = 10 b. x = 12 C. X = 6 2. Shown below are Ritz Glenn's scores, the mean, and the standard devia- tion of each three tests given to 500 applicants. Test . Ritz Glenn's Score Mean. S.D. Math 95 90.5 9.5 Science 88 85 10 English 90 88.6 5.5 On which test did Ritz Glenn stand highest? lowest?148 ELEMENTARY STATISTICS WITH COMPUTER APPLICATIONS 3. Prof. Y.A.G. a researcher at the University of the East, has collected in formation on millionaires, including their ages. Suppose the mean age of a sample of 32 millionaires is x = 56.5 years with a standard deviation of s = 14.2 years. a. Complete the following graph: x-3s 2s x-1s x x+1s x 2s x+3s 13.9 56.5 84.9 b. Apply the Chebyshev's theorem with k = 2 to make some observa- tions about the ages of the 32 millionaires. c. Repeat part (b) with k = 3.MEASURES OF VARIABILITY, SKEWNESS AND KURTOSIS 149 e'K'l___'_h_-.__ 4. The mean weight of 600 women in the age group 18-22 years 18 99 '5 pounds and the standard deviation is 5 pounds. a. At least, how many would you expect to be weighing between 89 and 109 pounds? b. Find the two values which must lie at least % of the data. 5- In a production process, the average weight of cans of_ corned heef is 30 grams and the standard deviation is 3 grams. What IS the wetght of a can with a z-score of 0.9