Statistics Book Exercises-Chapter3

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.

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.

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

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

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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.

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b. Calculate and interpret the geometric mean return.

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

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Section 3.4:

39.) Consider the following population data:

34

42

12

10

22

a. Calculate the range.

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b. Calculate MAD.

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c. Calculate the population variance.

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d. Calculate the population standard deviation.

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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?

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

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

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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?

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

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

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