Achievement objective S6-1
In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:
Plan and conduct investigations using the statistical inquiry cycle:
A. justifying the variables and measures used
B. managing sources of variation, including through the use of random sampling
C. identifying and communicating features in context (trends, relationships between variables, and differences within and between distributions), using multiple displays
D. making informal inferences about populations from sample data
E. justifying findings, using displays and measures.
- Uses the statistical inquiry cycle to conduct investigations
- Poses investigative questions
- Selects, uses and justifies variables and their measures to use in order to solve a problem. For example, if investigating how to improve the school canteen, students need to decide what ‘improve’ means and select data measures to capture improvement
- Selects and uses appropriate sampling methods, for example, systematic and simple random techniques (names drawn from a hat, dice, or random number generators)
- Uses a variety of data collection methods, such as web survey, face-to-face questionnaire, and automated computer logs
- Collects and manages data
- Uses appropriate statistical graphs and tables to explore the data and communicates relevant detail and overall distributions
- Explores summary, comparative, bivariate, and time series data
- Links multiple representations and sees the connections between them
- Writes and presents a concise and informative report that includes communicating features in context; relevant summary statistics, graphs and tables to support the findings of the investigation; quantitative and qualitative statements; informal inferences about a population from a sample; justified conclusions.
What is new/changed?
- Justifying variables and measures used
- Looking at the different sources of variation, for example, measurement variation
- Random sampling
- Sampling variation
- Informal inferences using informal decision criteria as evidence for making a claim which is based on an understanding of sampling variation
- Alternative explanations for observed patterns in the data
- Contextual knowledge plays an important role in the entire statistical inquiry cycle
Possible context elaborations
- CensusAtSchool – data collected by students, about students, for students – investigating comparative and bivariate situations using the CensusAtSchool database. For example, Do the bag weights of year 11 girls tend to be heavier than the bag weights of year 11 boys in the 2009 CensusAtSchool survey? Is there a relationship between heights of students and their neck circumference?
(ONLY good for PRACTICE - as students need to collect their own data for the assessment)
- Investigate the relationship between memory recall before learning memory recall skills and memory recall after learning memory skills
- Growing scatter plots – uses CensusAtSchool data and looks at relationships between neck and wrist circumferences
- Sleeping sheep – collecting reaction times, using a web-based application, for comparison
- You can’t fool me by giving me a cheap cola. Explores experiments and comparison.
- Do boy babies tend to be heavier at birth than girl babies? Comparisons using dot plots and box plot.
- Does practice make perfect? Relationships and comparisons using box plots and scatter plots
Students need to provide evidence of each component of the statistical enquiry cycle detailed in Explanatory Note 3 of the standard.
For this standard students will be working with a relationship question they have been given.
This standard requires students to be involved in planning the investigation and collecting their own data. An important part of the evidence is the plan component of the statistical enquiry cycle. In their plan students need to indicate what variables they will measure and describe how they will measure them. The description needs to include discussion on any possible sources of variation in the measurements and any actions they will take to ensure the data they collect is consistent.
Using data from a website such as Census at School is not appropriate because the student has not determined the measures or managed the sources of variation.
The student work needs to include the data they have collected.
Students need to be careful not to classify unusual points as outliers without appropriate justification.