BUS219 Chapter 3 - Given the following observations

BUS 219

Book Exercises - Chapter 3

Section 3.1

1.) Given the following observations from a sample, calculate the mean, the median, and the mode. Show your work.

8

10

9

12

12

Mean:

Median:

Mode:

Section 3.2:

20.) Using 500 observations, the following five-point summary was obtained for a variable.

Min	Q1	Median	Q3	Max
125	200	300	550	1300

a. Interpret Q1 and Q3.

·b. Calculate the interquartile range. Determine whether any outliers exist.

·c. Is the distribution symmetric? If not, comment on its skewness.

·Section 3.3:

34.) Suppose at the beginning of Year 1 you decide to invest $1,000 in a mutual fund. The following table shows the returns (in %) for the past four years.

Year	Annual Return
1	17.3
2	19.6
3	6.8
4	8.2

 

a. Calculate and interpret the arithmetic mean return.

·b. Calculate and interpret the geometric mean return.

c. How much money would you have accumulated by the end of Year 4?

·Section 3.4:

39.) Consider the following population data:

34

42

12

10

22

a. Calculate the range.

b. Calculate MAD.

·c. Calculate the population variance.

·d. Calculate the population standard deviation.

·Section 3.5:

51.) Consider the following summary measures for the annual returns for Stock 1 and Stock 2 over the past 13 years.

Stock 1: x? = 9.62% and s = 23.58%

Stock 2: x? = 12.38% and s = 15.45%

a. Which stock had the higher average return?

b. Which stock was riskier over this time period? Given your answer in part (a), is this result surprising? Explain.

c. Given a risk-free rate of 3%, which stock has the higher Sharpe ratio? What does this ratio imply?

·Section 3.6:

57.) Observations are drawn from a bell-shaped distribution with a mean of 20 and a standard deviation of 2.

a. Approximately what percentage of the observations fall between 18 and 22?

·b. Approximately what percentage of the observations fall between 16 and 24?

-c. Approximately what percentage of the observations are less than 16?