# Mathematics - annotated exemplars level 1 AS91036

## Investigate bivariate numerical data using the statistical enquiry cycle (1.11)

 Read the STANDARD TKI Mathematics and Statistics Assessment Resources Download all these exemplars and commentary (PDF, 955KB)

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 December 2020. This exemplar has been updated in its entirety.

### Low Excellence

Commentary
Student response

For Excellence, the student needs to investigate bivariate numerical data using the statistical enquiry cycle, with statistical insight.

This involves integrating statistical and contextual knowledge throughout the statistical enquiry cycle and may involve reflecting on the process or considering other explanations for the findings.

The evidence comes from the TKI assessment resource ‘Bivariate Smorgasbord’.

The student has planned and conducted an investigation using bivariate numerical data by working with a given relationship question (1), determining appropriate variables and measures (2), and managing sources of variation (3).

They have also gathered data (4) and selected and used appropriate displays (5). The student has also communicated the relationship in the data, including the strength and direction (6).

The student has integrated statistical and contextual knowledge (7). There is reflection on the process (8).

For a more secure Excellence, the student could strengthen the contextual discussion and reflection on the process. For example, the student could consider what effect different varieties of carrots could have on the relationship.

### High Merit

Commentary
Student response

Student 2 (PDF, 308KB)

For Merit, the student needs to investigate bivariate numerical data using the statistical enquiry cycle, with justification.

This involves linking aspects of the statistical enquiry cycle to the context and making supporting statements which refer to evidence, such as summary statistics, data values, trends or features of visual displays.

The evidence comes from the TKI assessment resource ‘Bivariate Smorgasbord’.

The student has planned and conducted an investigation using bivariate numerical data by working with a given relationship question (1), determining appropriate variables and measures (2), and managing sources of variation (3).

They have also gathered data (4) and selected and used appropriate displays (5). There is supporting evidence for the comments made about the strength and direction of the relationship (6).

The student has also started to incorporate some contextual knowledge (7).

To reach Excellence, the student could integrate contextual knowledge with the comments throughout the response and provide a more in-depth discussion about the features. The student could also reflect on the process.

### Low Merit

Commentary
Student response

Student 3 (PDF, 442KB)

For Merit, the student needs to investigate bivariate numerical data using the statistical enquiry cycle with justification.

This involves linking aspects of the statistical enquiry cycle to the context and making supporting statements which refer to evidence such as summary statistics, data values, trends or features of visual displays.

The evidence comes from the TKI assessment resource ‘Bivariate Smorgasbord’.

This student has planned and conducted an investigation using bivariate numerical data by working with a given relationship question (1), determining appropriate variables and measures (2), and managing sources of variation (3).

They have also gathered data (4), selected and used appropriate displays (5) and communicated the relationship in the data (6). There is supporting evidence for the comments made about the strength and direction of the relationship and unusual values (7).

For a more secure Merit, the student could strengthen the discussion on managing possible sources of variation, for example explaining why the scales were reset each time and the number of outside layers removed. The student would also need to strengthen their communication by, for example, justifying the comments made about the unusual value and linking these to the context.

### High Achieved

Commentary
Student response

Student 4 (PDF, 347KB)

For Achieved, the student needs to investigate bivariate numerical data using the statistical enquiry cycle.

This involves using each component of the statistical enquiry cycle to investigate bivariate numerical data.

The evidence comes from the TKI assessment resource ‘Bivariate Smorgasbord’.

The student has planned and conducted an investigation using bivariate numerical data by working with a given relationship question (1), determining appropriate variables and measures (2), and managing sources of variation (3).

They have also gathered data (4), selected and used appropriate displays (5) and communicated the relationship in the data (6).

To reach Merit, the student could justify the comments about the strength of the relationship. The student could also strengthen the discussion around the plan and managing sources of variation by explaining what accurate and inaccurate measurements mean in this situation.

### Low Achieved

Commentary
Student response

Student 5 (PDF, 390KB)

For Achieved, the student needs to investigate bivariate numerical data using the statistical enquiry cycle.

This involves using each component of the statistical enquiry cycle to investigate bivariate numerical data.

The evidence comes from the TKI assessment resource ‘Bivariate Smorgasbord’.

The student has planned and conducted an investigation using bivariate numerical data by working with a given relationship question (1), determining appropriate variables and measures (2), and managing sources of variation (3).

They have also gathered data (4), selected and used appropriate displays (5) and communicated the relationship in the data (6).

For a more secure Achieved, the student could clearly link the description of the relationship to the context of height and cubit length. This student could also provide more detail in their plan on how possible sources of variation were managed for the cubit measurements.

### High Not Achieved

Commentary
Student response

Student 6 (PDF, 215KB)

For Achieved, the student needs to investigate bivariate numerical data using the statistical enquiry cycle.

This involves using each component of the statistical enquiry cycle to investigate bivariate numerical data.

The evidence comes from the TKI assessment resource ‘Bivariate Smorgasbord’.

The student has worked with a given relationship question (1), determined appropriate variables and measures (2), gathered data (3), selected and used appropriate displays (4) and communicated the relationship in the data (5).

To reach Achieved, the student could explain how the height and weight were measured and identify and manage possible sources of variation.