# Mathematics and Statistics - annotated exemplar Level 3 AS91581

## Investigate bivariate measurement data (3.9)

 Read the STANDARD TKI Mathematics and Statistics Assessment Resources Download all these exemplars and commentary (PDF, 860KB)

This annotated exemplar is intended for teacher use only. The student work shown does not always represent a complete sample of what is required. Selected extracts are used, focused on the grade boundaries, in order to assist assessors to make judgements at the national standard.

Last updated June 2019.

All annotations have been altered to better illustrate the requirements of the standard.

### Low Excellence

Commentary
Student work extract

Student 1 (PDF, 171KB)

For Excellence, the student needs to investigate bivariate measurement data, with statistical insight.

This involves integrating statistical and contextual knowledge throughout the investigation process. It may include reflecting about the process, considering other relevant variables, evaluating the adequacy of any models, or showing a deeper understanding of the models.

This evidence is from a student’s response to the TKI task ‘Sport science’.

The student has posed an appropriate relationship question which is informed by research (1), and has also described the nature and strength of the relationship and related this to the context (2).

Contextual knowledge from the research (3) and statistical knowledge (4) have been integrated into the discussion about the features in the data and in the evaluation of the adequacy of the models (5).

Other relevant variables have been considered in the re-categorisation into ball and no ball sports (6).

This extract is from a student response which also included evidence of using the model to make a prediction and communicating findings in a conclusion, at an appropriate level to be awarded Excellence.

For a more secure Excellence, the student could have reflected on the process more deeply, for example by relating a visual inspection of the scatter graphs to the adequacy of the models, and/or linking the findings to further research.

### High Merit

Commentary
Student work extract

Student 2 (PDF, 211KB)

For Merit, the student needs to investigate bivariate measurement data, with justification.

This involves linking components of the statistical enquiry cycle to the context, and referring to evidence such as statistics, data values, trends, or features of visual displays in support of statements made.

This evidence is from a student’s response to the TKI task ‘Sport science’.

The student has posed an appropriate relationship question which is informed by research (1), and described the nature and strength of the relationship and related this to the context (2).

The description of the features has been justified by evidence from the data and displays (3), and the residuals have been used to support the comments on the appropriateness of the linear model (4).

The student has also linked the components of the statistical enquiry cycle to the context when communicating findings in a conclusion (5).

This extract is from a student response which also included evidence of using the model to make a prediction and justifying its accuracy, at an appropriate level to be awarded Merit.

To reach Excellence, aspects of the investigation could be supported with comments which demonstrate integration of contextual and statistical knowledge. For example, the student could consider whether the strength, direction and other features of the data are consistent with their own research.

### Low Merit

Commentary
Student work extract

Student 3 (PDF, 579KB)

For Merit, the student needs to investigate bivariate measurement data, with justification.

This involves linking components of the statistical enquiry cycle to the context, and referring to evidence such as statistics, data values, trends, or features of visual displays in support of statements made.

This evidence is from a student’s response to the TKI task ‘Sport science’.

The student has posed an appropriate relationship question which is informed by research (1), and described the nature and strength of the relationship and related this to the context (2).

The student has also identified features in the data and provided some support for statements made with evidence from the displays, and explanations have been related to the context (3).

An appropriate model has been found and used to make predictions, and there is some discussion about how accurate the predictions might be (4).

For a more secure Merit, the student would need to discuss other features of the displays, for example any unusual values, and strengthen the supporting evidence of statements with further evidence from the displays and data.

Stronger evidence of communicating findings in a conclusion would also be expected.

### High Achieved

Commentary
Student work extract

Student 4 (PDF, 440KB)

For Achieved, the student needs to investigate bivariate measurement data.

This involves showing evidence of using each component of the statistical enquiry cycle.

This evidence is from a student’s response to the TKI task‘Sport science’.

The student has posed an appropriate relationship question that is informed by research (1), selected and used appropriate displays (2), identified features in the data (3) and found an appropriate model (4).

They have also described the nature and strength of the relationship and related this to the context (5), used the model to make a prediction (6) and communicated their findings in a conclusion (7).

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 when communicating findings in a conclusion.

### Low Achieved

Commentary
Student work extract

Student 5 (PDF, 402KB)

For Achieved, the student needs to investigate bivariate measurement data.

This involves showing evidence of using each component of the statistical enquiry cycle.

The student has posed an appropriate relationship question (1), selected and used appropriate displays (2), identified features in the data (3) and found an appropriate model (4).

They have also described the nature and strength of the relationship and related this to the context (5), used the model to make a prediction (6) and communicated findings in a conclusion (7).

For a more secure Achieved, the posed question needs to be informed by contextual research about a possible relationship. There also needs to be more depth in the description of features in the data, particularly in relating descriptions to the context of the investigation.

### High Not Achieved

Commentary
Student work extract

Student 6 (PDF, 356KB)

For Achieved, the student needs to investigate bivariate measurement data.

This involves showing evidence of using each component of the statistical enquiry cycle.

This evidence is from a student’s response to the TKI task‘Sport science’.

The student has posed an appropriate relationship question (1), selected and used appropriate displays (2), identified features in the data (3), found an appropriate model (4) and used the model to make a prediction (5).

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 need to provide a conclusion.