| Year 10 Mathematics Term 1 Statistics Assignment |
Browns Plains State High School
| Unit | Statistics | Year | 2023 | Term | 1 |
| Student | Cynthia giramata | Teacher | |
| Learning area | Mathematics | Class | MAT101 |
| Technique | Extended response | ||
| Conditions | · To be submitted digitally
· Time allowed- 3 weeks · Resources- calculator, computer, internet, Excel Spreadsheets |
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| Task description | |||
| · Plan and conduct statistical investigations of situations that involve bivariate data; evaluate and report findings with consideration of limitations of any inferences. AC9M10ST05
· Analyse claims, inferences and conclusions of statistical reports in the media, including ethical considerations and identification of potential sources of bias. AC9M10ST01 · Compare data distributions for continuous numerical variables using appropriate data displays including boxplots; discuss the shapes of these distributions in terms of centre, spread, shape and outliers in the context of the data. AC9M10ST02 |
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| Task instructions | |||
| · Complete your assignment at home (only 3 lessons given for assignment)
· Type all your responses and insert necessary charts or screenshots in the relevant areas · Submit this fully edited Word document digitally through your class’s OneNote
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| Checkpoints | |||
| ☐ Week 6 Friday- Checkpoint 1- Part 1’s Questions 1-2 completed | |||
| ☐ Week 7 Friday- Checkpoint 2- Part 1 entirely and Part 2’s Question 1 completed | |||
| Due date | |||
| Week 8 Lesson 3 – Friday, 17th March, 2023 | |||
| Authentication strategies | |||
| · The teacher will provide 3 hours of class time for task completion. | |||
| · Students will provide documentation of their progress at indicated checkpoints. | |||
| · Students must submit a declaration of authenticity. | |||
| · The teacher will ensure class cross-marking occurs. | |||
I declare that the work submitted in this assessment is entirely my own. I also declare that I am fully aware of Browns Plains State High School’s Academic Policy with regards to timeous submissions of Drafts and the Final Copy of my assignment.
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Name Signature Date
Data representation — Written task
The following information is based on Australian Bureau of Statistics data and: https://www.abs.gov.au/statistics/people/education/education-and-work-australia/may-2022
https://www.education.gov.au/integrated-data-research/benefits-educational-attainment
Background information
Levels of participation in education and the labour market are frequently cited indicators of the wellbeing of young people. Research suggests that young people who are not fully engaged in education or work (or a combination of both) are at greater long-term risk of unemployment, cycles of low pay and employment insecurity. Participation in education and training, and engaging in work are also considered important aspects of developing individual capability and building a socially inclusive society.
Definitions
Employed full-time: employed persons who usually worked 35 hours or more a week (in all jobs) and those who, although usually working less than 35 hours a week, worked 35 hours or more during the reference week.
Employed part-time: employed persons who usually worked less than 35 hours a week (in all jobs) and either did so during the reference week, or were not at work in the reference week.
Unemployed: persons who were not employed during the reference week, and had actively looked for (and were available to start) full-time or part-time work at any time in the four weeks up to the end of the reference week. In this article, the unemployed excludes those who were studying part-time.
Not in the labour force: persons who were not in the categories ‘employed’ or ‘unemployed’.
Enrolled: refers to persons registered for a course of study in the particular reference period at an educational institution. People enrolled at the time of the survey were asked whether they were studying their course full-time or part-time.
School leavers: persons aged 15–19 years who attended school in 2008 but were not attending school prior to the survey date in May 2009.
Fully engaged: people who, in the survey reference week, were in full-time work or in full-time education, or in part-time work combined with part-time education.
Not fully engaged: includes people who, in the survey reference week, were working part-time (but not studying), unemployed (regardless of whether studying part-time), studying part-time (and not working) and not in the labour force (except those who were full-time students).
Part 1: Interpret and evaluate statistical reports
Relevant statistics:
Non-school qualifications and employment
People aged 15-74 years with a non-school qualification (certificate, diploma or degree) were more likely to be employed (79%) than those without a non-school qualification (58%).
The higher the qualification, the more likely people were to work full-time:
- 74% of men with a degree at bachelor level or above worked full-time, compared with 69% with a non-school qualification below bachelor level, and 44% with no non-school qualifications.
- 53% of women with a degree at bachelor level or above worked full-time, compared with 39% with a non-school qualification below bachelor level, and 23% with no non-school qualifications.
Source: Australian Bureau of Statistics, Education and Work, Australia May 2022
Source 1: Labour force status by non-school qualifications, by sex- May 2022
(a) All persons aged 15-74 years.
(b) Includes certificates I-IV and n.f.d., diplomas, advanced diplomas and associate degrees.
Source: Australian Bureau of Statistics, Education and Work, Australia May 2022
Question 1
Pick one gender from Source 1, create three different pie charts to represent the employment status in each education level. Use the Excel provided to generate the pie charts.
Hint: pie charts should show title, categories and percentages clearly
- Gender Chosen: Male/Female (Circle/Highlight the gender)
- Pie chart images attached:
| Pie Chart 1- Bachelor level and above |
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| Pie Chart 2- Below bachelor level |
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| Pie Chart 3- Non school qualification |
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Source 2: Median derived total annual income from wages and salaries for 30–64 years old not currently studying, by highest level of educational attainment, 2015–16
Source: Benefits of educational attainment, Australian Government, 2019
Question 2
Using the data from source 2, calculate the following related to Australians’ median annual income:
- Range:
- Inter-quartile range:
Source 3: the median cumulative lifetime earnings of people by age, depending on their level of educational attainment. Updated March, 2016.
Source: http://politicsthatwork.com/graphs/education-lifetime-earnings, 2016
Question 3
Do the above sources provided support the statement ‘Australians who did not complete post-secondary education are less likely to be employed and earn a median income’?
- Supports or Rejects (Highlight one)
- Identify two (2) points that support or reject the statement.
- It is true that people without much study can earn more money but from the sources provided we can see that the above sources provided support the statement ‘Australians who did not complete post-secondary education are less likely to be employed and earn a median income. As we saw in source 3 it shows that people with PhD earn $3,000,000 while people who just finished high school earn about $700,000. Source 1 as well proves evidence that supports this statement it shows in the graph people who are
ii.
Part 2: Graphing and comparing data
One Year 10 class conducted their own survey among family and friends who have left school. The class collected 27 responses that were then recorded on the table of survey responses below. Discuss the survey and the responses as a whole class.
Responses from class Learning or earning survey
| Survey number | Male/female | Age | Last year of schooling | Situation in the year after school | Highest qualification | Years in post-secondary education | Current situation | Yearly income | Industry |
| 1 | M | 28 | 12 | SFT | University | 8 | EFT | $96,000 | Other |
| 2 | F | 49 | 10 | EFT | TAFE | 1 | U | $12,600 | Retail |
| 3 | M | 38 | 11 | EPT | 11 | 0 | EPT/SPT | $23,000 | Hospitality |
| 4 | M | 54 | 10 | SFT | Apprenticeship | 4 | EFT | $71,000 | Transportation |
| 5 | M | 26 | 12 | U | TAFE | 3 | SFT | $10,400 | Other |
| 6 | M | 39 | 12 | SFT | University | 4 | EFT | $89,000 | Education |
| 7 | M | 39 | 10 | SFT | Traineeship | 1.5 | EFT | $46,800 | Banking/finance |
| 8 | M | 29 | 12 | EFT | University | 4 | EFT | $100,500 | Communications |
| 9 | F | 31 | 11 | SPT | 11 | 0 | U | $12,600 | Banking/finance |
| 10 | M | 48 | 10 | SFT | Apprenticeship | 2 | EPT | $39,000 | Retail |
| 11 | M | 28 | 11 | EPT/SPT | University | 3 | EFT | $88,000 | Communications |
| 12 | F | 22 | 12 | SFT | TAFE | 2.5 | EFT | $52,000 | Hospitality |
| 13 | M | 21 | 12 | SFT | TAFE | 1.5 | SFT | $10,400 | Hospitality |
| 14 | M | 41 | 12 | SFT | University | 7 | EFT | $150,000 | Communications |
| 15 | F | 42 | 12 | EPT | University | 5.5 | EFT | $123,000 | Communications |
| 16 | F | 31 | 12 | SFT | University | 6 | EFT | $118,000 | Other |
| 17 | F | 50 | 10 | NILF | 10 | 0 | NILF | $11,200 | Other |
| 18 | M | 50 | 12 | SFT | University | 10 | EFT | $122,000 | Other |
| 19 | F | 44 | 12 | SFT | University | 3.5 | EFT | $116,995 | Banking/finance |
| 20 | F | 44 | 11 | EFT | 11 | 0 | EFT | $140,000 | Retail |
| 21 | M | 24 | 10 | EFT | 10 | 0 | SPT | $7,900 | Retail |
| 22 | M | 21 | 10 | U | TAFE | 2 | EPT | $84,700 | Manufacturing |
| 23 | F | 43 | 12 | EFT | 12 | 0 | U | $12,600 | Manufacturing |
| 24 | M | 47 | 12 | SFT | University | 3 | EFT | $68,000 | Hospitality |
| 25 | F | 32 | 12 | SFT | Apprenticeship | 4 | EFT | $64,000 | Other |
| 26 | F | 51 | 11 | EPT/SPT | University | 4 | EFT | $78,000 | Health |
| 27 | M | 39 | 12 | SFT | University | 5 | EFT | $110,000 | Education |
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Key: SFT Studying full-time EFT Employed full-time EPT/SPT Employed part-time and studying part-time |
EPT Employed part-time and not studying SPT Studying part-time U Unemployed NILF Not in the labour force |
You will need to refer to the survey and table presented on the previous pages to answer the following questions.
Question 1
- Construct parallel box plots that best demonstrate the ‘yearly income’ of the people surveyed depending on whether they completed Year 12 or not.
Working space:
- Use a different way to display this data.
Question 2
Describe the data represented by the box .
Compare the box plot data
Question 3
A scatter plot has been constructed from the survey responses and is shown below.
Comment on the relationship between the two variables in the scatter plot.
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Question 4
On the scatter plot above, two data point, (A and B) have been identified as being ‘unusual’.
Provide an argument whether points A and B:
- represent valid data
- should be included in determining a relationship between yearly income and post-secondary study.
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They own good income and they did less school the reason why it’s unusual because the higher you study the more money you get. You about 3 years and have less money than the person who did study
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Instrument-specific marking guide (ISMG)
Criterion: Formulate
Assessment objectives
- select, recall and use facts, rules definitions and procedures
- comprehend mathematical concepts and techniques
- justify procedures and decisions by explaining mathematical reasoning
| The student work has the following characteristics: | Marks |
| • documentation of appropriate assumptions
• accurate documentation of relevant observations • accurate translation of all aspects of the problem by identifying mathematical concepts and techniques. |
3 – 4 |
| • statement of some relevant observations
• translation of simple aspects of the problem by identifying mathematical concepts and techniques. |
1 – 2 |
| • does not satisfy any of the descriptors above. | 0 |
Criterion: Solve
Assessment objectives
- select, recall and use facts, rules, definitions and procedures
- solve problems by applying mathematical concepts and technique
| The student work has the following characteristics: | Marks |
| • use of complex procedure to reach an accurate solution
• discerning application of mathematical concepts and techniques relevant to the task • appropriate use of technology. |
6 – 7 |
| • use of complex procedures to reach a reasonable solution
• application of mathematical concepts and techniques relevant to the task • appropriate use of technology. |
4 – 5 |
| • use of simple procedures to make some progress towards a solution
• simplistic application of mathematical concepts and techniques relevant to the task • superficial use of technology. |
2 – 3 |
| • isolated use of technology or procedures relevant to the task. | 1 |
| • does not satisfy any of the descriptors above. | 0 |
Criterion: Evaluate and Verify
Assessment objectives
- evaluate the reasonableness of solutions
- justify procedures and decisions by explaining mathematical reasoning
| The student work has the following characteristics: | Marks |
| • justification and explanation of procedures used and decisions made using mathematical reasoning
• evaluation of the reasonableness of solutions by considering the results, assumptions and/or observations • evaluation of relevant strengths and limitations of the solution and/or model. |
4 – 5 |
| • explanation of procedures used and decisions made
• statement about the reasonableness of solutions by considering the context of the task • statement about relevant strengths and limitations of the solution and/or model. |
2 – 3 |
| • statement about procedures, decisions and/or reasonableness of solutions | 1 |
| • does not satisfy any of the descriptors above. | 0 |
Criterion: Communicate
Assessment objectives
- communicate using mathematical, statistical and everyday language and conventions
| The student work has the following characteristics: | Marks |
| • correct use of appropriate mathematical, statistical and everyday language and conventions to develop the response
• coherent and concise organisation of the response, appropriate to the genre, including a suitable introduction, body and conclusion, which can be read independently of the task sheet. |
3 – 4 |
| • use of some appropriate mathematical, statistical and everyday language and conventions to develop the response
• adequate organisation of the response. |
1 – 2 |
| • does not satisfy any of the descriptors above. | 0 |
| YEAR 10 MATHEMATICS: UNIT 1: Statistics Assignment | Name:
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Purpose: To evaluate statements made in reports with regard to supporting data. To demonstrate understanding of parallel box plots and other data displays.
| A | B | C | D | E | |
| Analyse claims, inferences and conclusions of statistical reports in the media, including ethical considerations and identification of potential sources of bias. AC9M10ST01
Part 1 Q1-3
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Correctly display pie charts and accurately calculate range and inter-quartile range.
Provide discerning conclusion of how education affects future pay.
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Correctly display pie charts and accurately calculate range and inter-quartile range.
Provide a logical conclusion of how education affects future pay.
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Display correct pie charts partially and accurately calculate range and inter-quartile range.
Attempt to provide a conclusion of how education affects future pay.
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Attempt to create a pie chart and calculate range and inter-quartile range. | No attempt made |
| Plan and conduct statistical investigations of situations that involve bivariate data; evaluate and report findings with consideration of limitations of any inferences.
AC9M10ST05
Part 1 Q3
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Clearly and concisely interpret statements and data in detail to support a stance.
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Clearly explain how sources 1 and 2 support or reject a statistical statement.
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Correctly and logically identify two points that support or reject the statement
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Attempt to identify two points with minor errors in explanations
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No attempt made |
| Compare data distributions for continuous numerical variables using appropriate data displays including boxplots; discuss the shapes of these distributions in terms of centre, spread, shape and outliers in the context of the data. AC9M10ST02
Part 2 Q1-4 |
Classifies data as being valid. Uses data to make a choice whether to keep or reject unusual data values. | Describes and compares the data distribution presented in a box plot.
Correctly comprehends IQR.
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Correctly calculates five-number summary and constructs a box plot.
Calculates the interquartile range.
Describes the relationship between variables on a scatter plot. |
Calculates the range for a data set. Sorts data into relevant categories.
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Selects data from a report.
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