Preliminary Mathematics General – Displaying and Interpreting Data

Outcomes AssessedMGP-1 uses mathematics and statistics to compare alternative solutions to contextual problemsMGP-2 represents information in symbolic, graphical and tabular formMGP-7 determines an appropriate form of organization and representation of collected dataMGP-9 uses appropriate technology to organise information from a limited range of practical and everyday contextsMGP-10 justifies a response to a given problem using appropriate mathematical terminology

TaskRead 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.

1

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.

Most Common Length of a Word in Newspaper Articles

Number of Letters per Word Number of Words Total Letters1 4 42 14 283 22 664 10 405 7 356 9 547 10 708 15 1209 6 5410 1 10111213 2 26

Total 100 507

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 Criteria Marks

1a

2

1

Clear argument and well supported with points for and/or against suggesting appropriateness of articleIdentified as appropriate with weak support ORIdentifies as inappropriate with strong support

1b

4

321

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

4 of above 5 points3 of above 5 points2 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

1c

2

1

Describes as positively skewed and clearly indicates characteristics and features that support thisDescribes as positively skewed ORIndicates majority of data toward lower end/shorter words

1d321

All 3 measures are correct2 correct measures1 correct measure

1e

32

1

Identifies median with strong justificationIdentifies median with weak justification ORIdentifies mean or mode with strong justificationIdentifies median ORIdentifies mode with weak justification

1f 1 Correctly states range = 12

1g 1 Correctly gives sample standard deviation as 2.70 (to 2 decimal places). Must indicate correct SD with Sx or n-1.

3

2a

2

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 ORCorrectly described the type of sampling used.

2b

4

321

Table includes: Heading Score column and frequency column Tally column with corresponding frequencies

∑ f=1003 of above 4 points2 of above 4 points1 of above 4 points

2c

54321

Correctly calculated all 5 measures for own dataCorrectly calculated 4 measuresCorrectly calculated 3 measuresCorrectly calculated 2 measuresCorrectly calculated 1 measure

2d

2

1

Clearly described findings and supported these with mathematical features/measuresSatisfactory description linked to at least one statistical measure.

2e

5

4321

Correctly lists 5 number summaries for both sets of data, uses an appropriate scale and correctly constructs box-and-whisker plots for both sets of data4 of the above 5 points3 of the above 5 points2 of the above 5 points1 of the above 5 points

2f

3

2

1

Lists 2 appropriate similarities and 1 appropriate difference (or vice versa) supported with mathematical evidenceLists 1 appropriate similarity and 1 appropriate difference supported with mathematical evidence ORLists 2 appropriate differences supported with mathematical evidenceGives 1 appropriate difference supported with mathematical evidence ORLists various similarities and differences in mathematical measures without connecting to what they mean

Total Mark Awarded /37

4

5