Download Preliminary Display and Interpreting Data

Preliminary Mathematics General – Displaying and Interpreting Data
Outcomes Assessed
MGP-1 uses mathematics and statistics to compare alternative solutions to contextual problems
MGP-2 represents information in symbolic, graphical and tabular form
MGP-7 determines an appropriate form of organization and representation of collected data
MGP-9 uses appropriate technology to organise information from a limited range of practical and everyday
contexts
MGP-10 justifies a response to a given problem using appropriate mathematical terminology
Task
Read through the section of an article from the Sydney Morning Herald, Life &Style below. A random sample of 100 words
was selected (lying between the two solid lines) and a table constructed showing the number of words with 1, 2, 3,13
letters.
Princess Beatrice's wacky wedding hat goes for princely sum
The flamboyant hat worn by Princess Beatrice at last month's British royal wedding has sold for £81,100
($123,644) on internet auction site eBay.
Proceeds from the sale of the hat, designed by Irish milliner Philip Treacy will be split between two
charities: the United Nations Children's Fund, UNICEF, and British charity Children in Crisis.
The princess, the oldest daughter of Prince Andrew and a granddaughter of Queen Elizabeth II, provided
one of the most memorable moments of a dramatic day when she stepped out in the eccentric headwear,
likened to a giant pretzel.
Other royal-watchers compared the creation to a toilet seat and it has inspired its own Facebook page, "Princess Beatrice's ridiculous
royal wedding hat", which has a following of more than 143,000 people.
"I've been amazed by the amount of attention the hat has attracted," the princess said in a statement on the auction site.
"It's a wonderful opportunity to raise as much money as possible for two fantastic charities."
Treacy, who is now based in London, designed many of the hats on show at the April 29 marriage between Prince William and Kate
Middleton, which was watched by an estimated global audience of two billion.
The celebrated designer said he was "delighted, flattered and touched" by the 22-year old princess's decision to donate the hat to charity.
"I hope that people all over the world will be generous and that this hat will benefit many. A hat is a symbol of positivity," he added.
The piece is described on the site as "a unique sculptural celebratory headpiece" made of tea rose silk, adding: "This is a gravity defying
hat!"
"I hope whoever wins the auction has as much fun with the hat as I have," the young royal said.
http://www.smh.com.au/lifestyle/people/princess-beatrices-wacky-wedding-hat-goes-for-princely-sum-20110523-1ezbx.html
1
Most Common Length of a Word in Newspaper Articles
Number of Letters per Word
Number of Words
Total Letters
1
2
3
4
5
6
7
8
9
10
11
12
13
4
14
22
10
7
9
10
15
6
1
4
28
66
40
35
54
70
120
54
10
2
100
26
507
Total
1. Use the passage and information in the table to:
a) Discuss on the appropriateness of the chosen passage as a sample for determining the
most common length (number of letters) of a word used in newspaper articles.
(2 marks)
b) Draw a frequency histogram
(4 marks)
c) Describe the shape of the data
(2 marks)
d) Find the mean, median and mode.
(3 marks)
e) Determine the best measure of central tendency to indicate the most common length of a
word for this data. Justify your response (no more than three lines).
(3 marks)
f) Calculate the range.
(1 mark)
g) Calculate the standard deviation.
(1 mark)
2. Select an appropriate passage of 100 words from a newspaper that represents a fair sample to
determine the most common length of words used in the print media (e.g. Telegraph or Herald) and
include a copy of this article in your submission to the teacher.
a) Describe why you chose this passage as being a fair sample and describe the type of
sample that you used.
(2 marks)
b) Set up and complete a frequency distribution table for your article to show the number of
letters used in words in newspaper articles.
(4 marks)
c) Find the mean, median, mode, range and standard deviation for this data.
(5 marks)
d) Describe your findings on the most commonly used length of words in newspaper articles.
(2 marks)
e) Prepare five number summaries and hence, using an appropriate scale, draw
box-and-whisker plots for both sets of data (from questions 1 and 2).
(5 marks)
f) Use your box-and-whisker plots to compare and contrast the two sets of data.
(3 marks)
2
Marking guidelines
Your task will be assessed on how well you:
 Clearly show and accurately do your calculations
 Represent your information in tables and graphs
 Justify your responses
 Use appropriate mathematical terminology in discussing, describing, comparing and contrasting
 Use appropriate scales for graphs
Marking Criteria
Qn
Possible
Marks
2
1a
1
4
1b
Criteria
Marks
Clear argument and well supported with points for and/or
against suggesting appropriateness of article
Identified as appropriate with weak support OR
Identifies as inappropriate with strong support
 Appropriate scale on x- and y- axes
 Labelled x- and y- axes with score in centre of each
column
 Gap between vertical axis and first column
 No gaps between columns
 Correctly plotted columns
3
2
1
4 of above 5 points
3 of above 5 points
2 of above 5 points
Note: If a polygon was also drawn, it was ignored as long as the histogram was clearly labeled to show
understanding of which was which
2
Describes as positively skewed and clearly indicates
characteristics and features that support this
1c
1
Describes as positively skewed OR
Indicates majority of data toward lower end/shorter
words
1d
3
2
1
3
2
1e
1
1f
1g
1
1
All 3 measures are correct
2 correct measures
1 correct measure
Identifies median with strong justification
Identifies median with weak justification OR
Identifies mean or mode with strong justification
Identifies median OR
Identifies mode with weak justification
Correctly states range = 12
Correctly gives sample standard deviation as 2.70 (to 2
decimal places). Must indicate correct SD with Sx or n-1.
3
2
2a
1
4
2b
2c
2d
3
2
1
5
4
3
2
1
2
1
5
2e
4
3
2
1
3
2
2f
1
Clearly described sampling technique used as stratified,
systematic or random and described why the selected
article was an appropriate/typical article.
Clearly described why the article was appropriate OR
Correctly described the type of sampling used.
Table includes:
 Heading
 Score column and frequency column
 Tally column with corresponding frequencies
  f  100
3 of above 4 points
2 of above 4 points
1 of above 4 points
Correctly calculated all 5 measures for own data
Correctly calculated 4 measures
Correctly calculated 3 measures
Correctly calculated 2 measures
Correctly calculated 1 measure
Clearly described findings and supported these with
mathematical features/measures
Satisfactory description linked to at least one statistical
measure.
Correctly lists 5 number summaries for both sets of data,
uses an appropriate scale and correctly constructs boxand-whisker plots for both sets of data
4 of the above 5 points
3 of the above 5 points
2 of the above 5 points
1 of the above 5 points
Lists 2 appropriate similarities and 1 appropriate
difference (or vice versa) supported with mathematical
evidence
Lists 1 appropriate similarity and 1 appropriate difference
supported with mathematical evidence OR
Lists 2 appropriate differences supported with
mathematical evidence
Gives 1 appropriate difference supported with
mathematical evidence OR
Lists various similarities and differences in mathematical
measures without connecting to what they mean
Total Mark Awarded
4
/37
5