# Mathematics and Statistics - annotated exemplar Level 3 AS91581 (A)

## Investigate bivariate measurement data (3.9A)

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 See EXEMPLAR B for this standard TKI Mathematics and Statistics Assessment Resources Download all these exemplars and commentary (PDF, 1.2MB)

### Low Excellence

Commentary
Student response

Student 1 (PDF, 216KB)

For Excellence the student is required to investigate bivariate measurement data, with statistical insight. This involves integrating statistical and contextual knowledge throughout the investigation process, and may include reflecting about the process; considering other relevant variables; evaluating the adequacy of any models, or showing a deeper understanding of the models.

An appropriate relationship question has been implied. The choice of different pairs of variables should have been considered (1). Appropriate displays have been selected and used (2).

Features of the data have been identified, and the nature and strength of the relationship with regard to visual aspects of the scatter about the regression line have been described in context. Comments indicate that the context of high performance sport has been considered (3).

An appropriate model has been found and justified. The model has been used to make predictions. The appropriateness of a linear model has been considered and there are some contextual comments about the predictions (4).

An additional model has been considered. The appropriateness of the new model and accuracy of the predictions using this model have been compared with the linear model (5).

Findings have been communicated in a conclusion and comments demonstrate an understanding of the context.  Issues related to specific sports and the age of the competitors could have been considered (6).

There is evidence of investigating bivariate measurement data with statistical insight in the integration of contextual knowledge.

For a more secure Excellence the student could have explored the relationship for male athletes, or could have considered investigating further particular sports.

### High Merit

Commentary
Student response

Student 2 (PDF, 224KB)

For Merit the student is required to investigate bivariate measurement data, with justification. This involves linking components of the statistical enquiry to the context, and referring to evidence such as statistics, data values, trends, or features of visual displays in support of statements made.

An appropriate relationship question has been posed. There is some contextual reflection on the nature of the data. The choice of a different pair of variables has been considered (1). Appropriate displays have been selected and used (2).

Features of the data have been identified and the nature and strength of the relationship have been described in context. There is some contextual discussion on features of the relationship (3).

An appropriate model has been found and justified. The model has been used to make predictions. There is contextual discussion about the predictions (4).

The student has acknowledged that they appear to have found a linear relationship between the variables, but that this does not imply causation (6).

Findings have been communicated, but there is no clear link to a purpose for the investigation. There has been some contextual consideration with provision of some background information (7).

There is evidence of investigating bivariate measurement data with justification in the provision of contextual evidence to support statements for components of the statistical enquiry cycle.

To reach Excellence all aspects of the investigation would need to be supported with reflective comments which demonstrate a deeper contextual understanding, supporting a clearer purpose of the investigation.

### Low Merit

Commentary
Student response

Student 3 (PDF, 212KB)

For Merit the student is required to investigate bivariate measurement data, with justification. This involves linking components of the statistical enquiry to the context, and referring to evidence such as statistics, data values, trends, or features of visual displays in support of statements made.

A relationship question has been implied. The variable selection has been justified and there is contextual consideration of the data source (1). Appropriate displays have been selected and used (2).

Features of the data have been identified and the nature and strength of the relationship have been described in context, including considering unusual features. Some contextual reasons have been used to justify comments (3).

An appropriate model has been found and justified. The model has been used to make predictions. There is a contextual comment about the predictions (4).

The student has considered that there may be differences in the relationship being investigated for male and female athletes. Two further models have been found and used to make predictions which are compared with the predictions made using the model for the entire group (5). Findings have been communicated (6).

There is evidence of investigating bivariate measurement data with justification in the provision of contextual evidence to support statements for components of the statistical enquiry cycle.

For a more secure Merit there would be more contextual discussion on key aspects such as how lean body mass affects an athlete’s performance in difference sports, and a clear indication of the purpose of the investigation.

### High Achieved

Commentary
Student response

Student 4 (PDF, 203KB)

For Achieved the student is required to investigate bivariate measurement data. This involves showing evidence of using each component of the statistical enquiry cycle.

An appropriate relationship question has been posed. The explanatory and response variables have been identified (1). Appropriate displays have been selected and used (2).

Features of the data have been identified and the nature and strength of the relationship have been described in context (3).

Appropriate models have been found and have been used to make predictions (4).

The student has considered another pair of variables and compared the strength of this relationship with the original investigation (5).

Findings have been communicated in a conclusion. There is some contextual reasoning in the discussion, but this is not supported (6).

There is evidence of investigating bivariate measurement data in the use of each component of the statistical enquiry cycle.

To reach Merit the student would need to provide more in the way of contextual references to support statements made. There would need to be some evidence that other background research material had been considered.

### Low Achieved

Commentary
Student response

Student 5 (PDF, 211KB)

For Achieved the student is required to investigate bivariate measurement data. This involves showing evidence of using each component of the statistical enquiry cycle.

An appropriate relationship question has been implied. The explanatory and response variables have been identified.  A simple purpose which relates to the Australian Institute of Sport has been identified (1). Appropriate displays have been selected and used (2).

Features of the data have been identified and the nature and strength of the relationship with regard to visual aspects of the scatter about the regression line have been described in context. Comments are limited in terms of contextual understanding (3).

An appropriate model has been found and it has been used to make predictions. There is limited discussion about the predictions (4).

Findings have been communicated in the conclusion and linked to the purpose of the investigation (5).

There is evidence of investigating bivariate measurement data in the use of each component of the statistical enquiry cycle.

For a more secure Achieved there would have been more depth in the description of the relationship and features of the display, particularly with respect to relating descriptions to the context of the investigation.

### High Not Achieved

Commentary
Student response

Student 6 (PDF, 187KB)

In order to achieve the standard the student is required to investigate bivariate measurement data. This involves showing evidence of using each component of the statistical enquiry cycle.

An appropriate relationship question has been implied.  The explanatory and response variables have been identified (1). Appropriate displays have been selected and used (2).

Some features of the data have been identified and the nature of the relationship has been described in context. The strength of the relationship relies on the value of the correlation coefficient, rather than referring to the visual aspect of scatter about the regression line (3).

An appropriate model has been found and it has been used to make predictions (4).

Findings have been not been communicated clearly in a conclusion.

The requirements for Achieved have not been met because the description of the strength of the relationship needs to refer to visual aspects of scatter about the regression line, rather than just rely on the value of the correlation coefficient. There is no conclusion.

To reach Achieved the student would need to have described the strength of the relationship by discussing visual aspects of scatter about the regression line in context. They would also have needed to provide a conclusion.