Claudia Pena
September 14, 2023
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.
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:
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: x̄ = 9.62% and s = 23.58%
Stock 2: x̄ = 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?
·
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