Outline and describe (with suitable examples) the different types of graphs, charts diagrams and tables used in statistical modelling and reporting. As a minimum, explain the circumstances in which you would use each of the following forms of visual presentation and why you would use them in that situation:
• Pie chart
• Bar chart
• Diagram
• Table
• Line graph
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The pie chart is used to display portions as a total
Simple bar chart shows a summary of one set of data
Pictogram is a visual form using a symbol relevant to the data shown
Shoe Like Disliked
Running 36 6
Cross-Trainer 45 8
Formal 27 10
Hiking 19 5
Work Boot 29 7
A Histogram is a column chart that shows frequency data
Discrete data is displayed on the polygon in the form of a graph
Question 2.
Brisbane North Pty Ltd has the following portfolio of assets:
Shares in mining companies $135,000
Shares in services industry companies $210,600
Government bonds $70,000
Business premises $950,400
Assessment task:
• Present the data as a pie chart
• Present the data as a bar chart
• Compare the presentation methods of a pie and a bar chart and state which method you would use in this example and why.
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Question 3.
Briefly explain the following and illustrate with examples where necessary:
• Frequency distribution
• The essential characteristics of class intervals
• Ogive
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Question 4.
The following unsorted list of the ages of students enrolled in a business course has been extracted from the local TAFE’s records:
24, 31, 45, 28, 24, 18, 18, 33, 34, 45, 44, 24, 31, 45, 44, 26, 24, 22, 21, 18, 33, 32, 41, 44.
Assessment task:
• Array the data
• Organise the data in a ungrouped frequency scale
• Construct a grouped frequency distribution
• Construct a frequency histogram and ogive of the data
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Question 5.
Bracken Ridge Pty Ltd has 50 representatives throughout Australia. The following table shows the distribution of representatives by sales last financial year.
Sales No. of representatives
$100,000 to $200,000 4
$200,000 to $300,000 9
$300,000 to $400,000 19
$400,000 to $500,000 13
$500,000 to $600,000 5
Assessment task:
• Calculate the mean sales performance of the representatives
• Determine the median class interval
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Question 6.
The following information has been extracted from the sales records of Bracken Ridge Suppliers Ltd.:
Value of Sales Order Mid point* Number of Orders
0 to 500 350 65
500 to 1000 850 35
1000 to 1500 1150 20
1500 to 2000 1750 12
2000 to 2500 2350 8
2500 to 3000 2750 2
* The mid point in each case has been calculated as the median of each range of observations.
Assessment task:
Calculate the:
• Mean sales
• Standard deviation of the population using a financial calculator or spreadsheet.
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Question 7.
Explain probability theory by making references to three types of probability and Venn diagrams.
Illustrate your explanation using examples and diagrams where necessary.
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Question 8.
Calculate the probability for each of the following:
a. The probability that the salesperson will sell a table is 3/9 and the probability that he will sell a chair 4/9. What is the probability that he will sell a table and a chair?
b. A coin is tossed and a card is drawn a pack of 52 playing cards. What is the probability that a coin will be a head and the card will be a heart? Remember there are 4 types of cards in a set: hearts, spades, clubs and diamonds. Are these events dependent or independent?
c. You will be going to skiing this week-end. The probability that it will snow this week-end is 25% and probability that if it snows there will be sufficient snow on the slopes is 80%. What is the probability that it will snow and you will ski.
d. If you throw coin three times. What is the probability of two tails on the first two coins and a head on the last? Are these events independent?
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