Week 1: Introduction to Statistics and Visual Presentation of Data
Task 1:
Define population and sample. Explain why sample is preferred than population. Which Australian Government Organisation surveys the total population?
Task 2:
Provide some methods of collecting primary data. What are the advantages of collecting secondary data? From information source can be used to collect secondary data?
Task 3:
Develop a questionnaire model (10 questions) and conduct a survey on the topic, "Does Academies Australasia require entertainment facilities for the students?" How questionnaire can assist to collect statistical data?
Task 4 - Frequency Distribution:
Below is a list of ages of students enrolled on a part-time business course:
|
20
|
17
|
29
|
30
|
22
|
31
|
|
19
|
23
|
27
|
21
|
18
|
17
|
|
19
|
19
|
19
|
22
|
23
|
18
|
|
24
|
25
|
20
|
19
|
18
|
22
|
Required:
a) Array the data
b) Organise the data in an ungrouped frequency distribution
c) Construct a grouped frequency distribution, in groups of size three
d) Construct a histogram and draw a polygon (frequency curve) of the data
Task 5:
Cumulative frequency:
The number of repairs per week over a six-month period for a camera store are given below:
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4
|
8
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13
|
10
|
2
|
6
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4
|
7
|
9
|
16
|
17
|
11
|
8
|
|
6
|
9
|
15
|
6
|
13
|
11
|
3
|
7
|
2
|
14
|
12
|
6
|
4
|
Required:
a) Array the data
b) Construct a grouped frequency distribution, in groups of size of four
c) Prepare a Histogram and Polygon
d) Calculate Cumulative Frequency
e) Identify when the camera store earned maximum revenue from repairs.
Task 6:
a) Pictograph
The following table shows the number of computers sold by a company for the first week of January to March. Construct a pictograph for the table.
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Month
|
January
|
February
|
March
|
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Number of computers
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4
|
6
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5
|
b) Tree diagram:
You are at a carnival. One of the carnival games asks you to pick a door and then pick a curtain behind the door. There are 3 doors and 4 curtains behind each door. How many choices are possible for the player?
Present the answer through a tree diagram.
Week 2: Measures of Central Tendency
Task7:
Calculation of Mean, Median and Mode from grouped date:
Number of complaints per week received by Radio Crazy in a 12 week rating period:
|
No of complaints
|
Midpoint (m)
|
No of weeks
(f)
|
fm
|
Cumulative Frequency
|
|
0-9
|
|
3
|
|
|
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10-19
|
|
5
|
|
|
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20-29
|
|
2
|
|
|
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30-39
|
|
1
|
|
|
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40-49
|
|
1
|
|
|
|
|
|
|
|
|
Required:
a) Calculate the mean
b) Calculate the median class
c) Calculate the modal class
d) What remedial actions the management can take from the above findings?
Week 3: Measure of Dispersion
Task8:
Below is the same of the points scored by each team in the 2013 NRL Premiership:
a) What is range?
|
Team
|
Points Scored
|
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Melbourne
|
521
|
|
Manly
|
539
|
|
Brisbane
|
511
|
|
Wests
|
519
|
|
St George
|
483
|
|
New Zealand
|
504
|
|
Nth Qld
|
532
|
|
Newcastle
|
478
|
|
Canterbury
|
449
|
|
Sth Sydney
|
531
|
|
Sydney
|
417
|
|
Penrith
|
430
|
|
Cronulla
|
428
|
|
Parramatta
|
385
|
|
Canberra
|
423
|
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Gold Coast
|
363
|
Task 9: Mean, Mean Deviation, Standard Deviation, Variance and Range (Grouped Data):
The following table shows the distribution of income of the 50 employees at an Adelaide Freight Company:
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Income $'000
|
m
|
No of Employees
|
fm
|
Im- I
|
fIm- I
|
Im- I²
|
fIm- I²
|
|
20 - 25
|
|
5
|
|
|
|
|
|
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25 - 30
|
|
6
|
|
|
|
|
|
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30 - 35
|
|
15
|
|
|
|
|
|
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35 - 40
|
|
10
|
|
|
|
|
|
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40 - 45
|
|
8
|
|
|
|
|
|
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45 - 50
|
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2
|
|
|
|
|
|
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50 - 55
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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Week 4: Correlation and Regression:
Task 10:
Calculate and describe the correlation coefficient between advertising (x) and sales (y):
Task 11:
The higher the aggregate running time of a particular machine, the higher the number of work hours required for maintenance. Below are the results of a survey on selected machines.
|
Machine No
|
Running time (hrs)
|
Hours Maintenance
|
|
1
|
60
|
5
|
|
2
|
45
|
4
|
|
3
|
120
|
8
|
|
4
|
80
|
5
|
|
5
|
110
|
12
|
Required: Estimate the maintenance hours required for a machine that has been used for 100 hours.
Task 12:
Estimate sales level for an expenditure of $13,000 on advertising from the following data:
|
Advertising ($'000)
X
|
Sales ($'000)
y
|
xy
|
x2
|
|
10
|
200
|
|
|
|
11
|
230
|
|
|
|
12
|
250
|
|
|
|
14
|
270
|
|
|
|
15
|
280
|
|
|
|
16
|
300
|
|
|
|
|
|
|
|
Task 13
A teacher suspects that lower attendance at statistics classes may be related to lower final examination scores in that subject. The final examination scores of various groups of students are shown as follows:
|
Number of classes missed
|
Final Exam Score (%)
|
|
0
|
80
|
|
1
|
85
|
|
2
|
77
|
|
3
|
71
|
|
4
|
61
|
|
5
|
62
|
|
6
|
52
|
Required:
a) Plot a scatter diagram of the variables "Class Missed" against "Exam Scores"
b) From your scatter diagram would you expect the correlation coefficient to be positive or negative? Explain your answer in terms of the variables in the diagram
c) Calculate the value of the product moment correlation co-efficient
Week 5: Probability
Task 14:
All customers of Chocmelt Ltd purchase online. When buying, they provide customer details (include sex and age). The profile of Chocmelt Ltd has been determined as:
|
Age
|
Under 20
|
20 - 40
|
40 - 60
|
Over 60
|
|
Male
|
20
|
75
|
30
|
25
|
|
Female
|
30
|
75
|
70
|
25
|
|
Total
|
50
|
150
|
100
|
50
|
(i) What is the probability that next customer order to be received will be from a male?
(ii) What is the probability that the next customer who orders is 40 years or older?
(iii) What is the probability that the next customer order received is from a female between 20 and 40?
(iv) What is the probability that the 1st customer order received is from a female and the 2nd customer is a male?
Task 15:
Explain Mutually Exclusive and dependent events. Draw a Venn diagram to make a visual presentation.
Week 6: Normal Distribution and Time Series & Trend Analysis
Task 16: Normal Distribution
Limptons Laboratories has the following sales figures:
Mean = $35,000 Standard Deviation = $6,000
The sales form an approximate normal curve.
Required:
a) What is the probability that Limptons will achieve a sales level greater than $32,000?
b) What is the change that sales will not be less than $20,000 and not greater than $44,000?
c) Above what level are the top 20% of sales targets?
Task 17:
The monthly sales of Zoom Co Pty Ltd form an approximate normal curve with a mean of $20,000 and standard deviation of $3,000.
Required:
a) The proportion of sales greater than $26,000
b) The proportion of sales less than $17,000
c) The proportion of sales between $17,000 and $23,000
Task 18
In formulating a budget, the value of sales is expected to be $1.2 million, with a standard deviation of $200,000.
Required:
a) What is the probability that the sales will be below $900,000?
b) What is the probability that the sales will be above $1.6 million?
c) What is the probability that the sales will be between $1 million and $1.4 million?
Task 19: Time Series & Trend Analysis
a) Plot the following data freehand and estimate sales for 2011:
|
Annual soft drink sales
($'000,000
|
2001
|
2002
|
2003
|
2004
|
2005
|
2006
|
2007
|
2008
|
2009
|
|
13
|
15
|
17
|
18
|
19
|
20
|
20
|
21
|
22
|
Week 7: Ratio Analysis
Task 20:
The following information is a condensed version of the financial statements for Enchanting Florist Ltd for the two years ended 30 June 2012 and 30 June 2013.
|
|
30 June 2012
|
30 June 2013
|
|
Sales (all on credit)
|
550,000
|
650,000
|
|
Cost of goods sold
|
200,000
|
280,000
|
|
Depreciation
|
40,000
|
40,000
|
|
Interest
|
20,000
|
25,000
|
|
Other expenses
|
100,000
|
110,000
|
|
Total expenses
|
360,000
|
455,000
|
|
Net profit before tax
|
190,000
|
195,000
|
|
Income tax
|
57,000
|
59,000
|
|
Net profit after tax
|
133,000
|
136,000
|
1. Calculate the following ratios for each year:
(a) Liquid ratio
(b) Net profit ratio
(c) Times interest cover
(d) Earnings per share
(e) Price Earnings Ratio
(f) Return on equity (shareholder's funds)
(g) Debtor collection period (turnover rate)
(h) Inventory turnover
2. Compare and explain the link between the movement in the earnings per share and the price earnings ratio. What may explain the difference in the movement in these two ratios?
3. Give two actions that the business may have taken to improve the debtor turnover rate.
Task 21:
You are interested to research on the changes of interest rate on home loan for last 5 years in Australia. Conduct research on Reserve Bank of Australia, put your findings on a Line Graph and describe the trend.
Task 22:
When you are filing statistical documents, what factors should be considered when deciding the filing order? How can you ensure the security of both soft copy and hard copy data base?
Task 23:
"Validate Data helps identify suspicious and invalid cases, variables, and data values in the active data set" - Based on this statement why statistical analysis are required to be validated.