**STAT20029 (T2,2020) Questions:**

**Week 3**

**Review problem 3.1**

RP3-1: The Australian Census of Population and Housing asks every household to report information on each person living in the house. Suppose that, for a sample of 30 households, the number of persons living in each was reported as follows. Compute the mean, median and mode for these data and interpret them in a brief plain-language report.

**Activity 3-1**

Activity 3-1: A sample of returns from two portfolios (in percent) is given below:

Year Portfolio A (%) Portfolio B (%)

1 6 9

2 8 12

3 0 -3

**Activity 3-2**

Activity 3-2: The following return were realized on an investment over a 5year period of two stocks:(a) Compute the geometric mean of each stock.

Year Rate of return of stock 1 Rate of return of stock 2

1 0.10 -0.15

2 0.22 - 0.20

3 0.06 0.15

4 -0.05 -0.08

5 0.20 0.50

**Practice Problem 3.9(a, b & c)**

PP3-9 : A data set contains the following eight sample values.

4 3 0 5 2 9 4 5

- Calculate the range.
- Calculate the sample variance.
- Calculate the sample standard deviation.

**Practice Problem 3.8(b &c)**

PP3-8: A data set contains the following seven values.

6 2 4 7 8 3 5

- Calculate the population variance.
- Calculate the population standard deviation.

**Review Problem 3.4**

RP3-4 : Suppose stock X costs an average of $13.21 per share and has shown a standard deviation of $5.28 for the past 30 days. Suppose stock Y costs an average of $2.52 per share and has shown a standard deviation of $0.50 for the past 30 days. Use the coefficient of variation to determine the variability for each stock. Based on the coefficient of variation, which is the riskier stock?

**Activity 3.3**

Activity 3.3: Approximate the sample mean and standard deviation of the following data.

**Class Fre(f)**

–20 up to –10 8

–10 up to 0 21

0 up to 10 43

10 up to 20 48

20 up to 30 25

30 up to 40 15

Total 160

**Activity 3.4**

Activity 3.4: Given the following sample frequency distribution

**Class Frequency**

[30, 40) 13

[40, 50) 19

[50, 60) 23

[60, 70) 9

[70, 80) 5

- i) Find the approximate mean
- ii) Find the approximate standard deviation

**Review Problem 3.3**

RP3-3: The Australian Census of Population and Housing asks for each resident’s age. Suppose that a sample of 40 households taken from the census data showed the age of the first person recorded on the census form as follows. Compute Q1, Q3, and the interquartile range of these data.

42 29 31 38 55 27 28 33 49 70

25 21 25 38 47 63 22 38 52 50

41 19 22 29 34 81 52 26 35 38

29 31 48 26 33 42 24 58 40 32

**Review Problem 3.7**

RP3-7: According to the Australian Taxation Office, the average taxable income in an affluent suburb of Sydney is $94 720. Suppose the median taxable income in this area is $90 050 and the mode is $89 200. Is the distribution in this area skewed? If so, how? Which of these measures of central tendency would you use to describe these data? Why?

**Practice Problem 3.9(d)**

PP3-9(d): A data set contains the following eight values.

4 3 0 5 2 9 4 5

Calculate IQR and draw a box and whisker plot.

**Practice Problem 3.15**

PP3-15: A survey of drivers asked respondents to list the age in years of the vehicle that they predominantly drive. The following data represent a sample of 18 responses provided. Use the data to construct a box and whisker plot. List the median, Q1, Q3, the endpoints. Are any outliers present in the data?

1 3 8 5 8 4 9 11 4

3 17 3 15 9 7 5 4 2

**Practice Problem 3.13**

PP3.13: An employment agency is concerned that some of its clients for whom it has found part-time work are not receiving enough hours of employment. It examines a sample of clients and asks them to report how many hours they had worked in the last month. The agency notes that the data are not normally distributed. If the mean hours worked is 38 and the standard deviation is 6 hours, what proportion of values would fall between 26 hours and 50 hours? What proportion of values would fall between 14 hours and 62 hours? Explain your findings in simple terms to the employment agency’s management team.

**Activity 3.5**

Activity 3-5: A sample of returns from two portfolios (in percent) is given below:

**Year Portfolio A Portfolio B**

1 8 -1

2 3 5

3 -2 4

4 5 9

5 6 6

6 7 4

(a) Find the mean value and standard deviation of returns for each of the portfolios.

(b) Find the correlation coefficient of returns between the portfolios.

(c) Find the geometric mean rate of return of each of the portfolios.

(d) Which portfolio is preferable? Why?

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