Can you help me with problem 3.2?

122 CHAPTER 3 | Numerical Descriptive Measures EXAMPLE 3.10 Continuing with the More Descriptive Choices scenario, you wish to explore the effects of each Computing combination of Fund Type, Market Cap, and Risk Level on measures of past performance. One Descriptive measure of past performance is the three-year return percentage. Compute the mean three-year Statistics Using return percentage for each combination of Fund Type, Market Cap, and Risk Level. Multidimensional SOLUTION A multidimensional contingency table (see Section 2.6) computes the mean three- Contingency Tables year return percentage for each combination of the three variables. FIGURE 3.6 Mean 3YrReturn Risk Level Excel multidimensional Fund Type Low Average High Grand Total contingency tables for Growth 9.87 9.06 6.64 8.51 Large 10.22 10,43 9.79 10.30 the mean three-year MidCap 8.93 6.86 5.78 6.93 ntages for Small 9.09 7.43 5.99 Value 7.76 6.41 4.13 6.84 each combination of Large 7.82 6.49 5.02 7.29 fund type, market cap, MidCap 7.87 7.05 2.22 6.69 and risk level Small 6.38 5.60 4.63 5.39 Grand Total 8.66 8.21 6.25 7.91 The three-year return is higher for low-risk funds than average-risk or high-risk funds for both the growth funds and value funds. However, this pattern changes when Market Cap cat- egories are considered. For example, the three-year return percentage for growth funds with average risk is much higher for large cap funds than for midcap or small market cap funds. Also, for value funds with average risk, the three-year return for midcap funds is higher than the return for large funds. PROBLEMS FOR SECTIONS 3.1 AND 3.2 LEARNING THE BASICS c. Calculate the Z scores. Are there any outliers? 3.1 The following set of data is from a sample of n = 5: d. Describe the shape of the data set. 74982 3.4 The following set of data is from a sample of n = 5: a. Calculate the mean, median, and mode. 7-5-879 b. Calculate the range, variance, standard deviation, and coeffi- a. Calculate the mean, median, and mode. cient of variation. b. Calculate the range, variance, standard deviation, and coeffi- c. Calculate the Z scores. Are there any outliers? cient of variation. d. Describe the shape of the data set. c. Calculate the Z scores. Are there any outliers? 3.2 The following set of data is from a sample of n = 6: d. Describe the shape of the data set. 7 4 9 7 3 12 3.5 Suppose that the rate of return for a particular stock during a. Calculate the mean, median, and mode. the past two years was 10% for one of the years and 30% for the b. Calculate the range, variance, standard deviation, and coeffi- other year. Compute the geometric rate of return per year. (A rate cient of variation. of return of 10% is recorded as 0.10, and a rate of return of 30% is c. Calculate the Z scores. Are there any outliers? recorded as 0.30.) d. Describe the shape of the data set. 3.6 Suppose that the rate of return for a particular stock during the 3.3 The following set of data is from a sample of n = 7: past two years was 20% for one of the years and -30% for the other 12 7 4 9 0 7 3 year. Compute the geometric rate of return per year. a. Calculate the mean, median, and mode. b. Calculate the range, variance, standard deviation, and coeffi- cient of variation