# Mathematics - annotated exemplars level 1 AS91035

## Investigate a given multivariate data set using the statistical enquiry cycle (1.10)

 Read the STANDARD TKI Mathematics and Statistics Assessment Resources Download all these exemplars and commentary (PDF, 298KB)

### Low Excellence

Commentary
Student response

Student 1 (PDF, 67KB)

For Excellence, the student needs to investigate a given multivariate data set 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.

This student’s evidence is a response to the TKI assessment resource ‘Sporting success’.

This student has posed an appropriate comparison question (1), selected and used appropriate displays (2), given summary statistics (3), discussed features of the distributions comparatively (4) and communicated an informal inference in their conclusion (5). Comments are justified with reference to the visual displays of the data and contextual knowledge is integrated throughout the response.

For a more secure Excellence, the student would need to integrate contextual knowledge more deeply, for example, by more closely linking the data points to the different teams in each hemisphere and the type of competition: overseas tour matches, the four nations matches or world cup matches.

### High Merit

Commentary
Student response

Student 2 (PDF, 66KB)

For Merit, the student needs to investigate a given multivariate data set 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.

This student’s evidence is a response to the modified TKI assessment resource ‘Sporting success’.

This student has posed an appropriate comparison question (1), selected and used appropriate displays (2), given summary statistics (3), discussed features of the distributions comparatively (4) and communicated an informal inference in their conclusion (5). Comments are justified throughout the response with reference to the visual displays of the data.

To reach Excellence, the student would need to integrate contextual knowledge with the comments throughout the response.

### Low Merit

Commentary
Student response

Student 3 (PDF, 44KB)

For Merit, the student needs to investigate a given multivariate data set 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.

This student’s evidence is a response to the modified TKI assessment resource ‘Get Online’.

This student has posed an appropriate comparative question (1), selected and used appropriate displays (2), given summary statistics (3), discussed features of the distributions comparatively (4) and communicated an informal inference in their conclusion (5). Some comments are justified with reference to the visual displays of the data.

For a more secure Merit, the student would need to strengthen the justification of the features of the distributions already described. The student could also consider other features, for example, the overlap of the boxes, the spread of the middle 50% and the skew.

### High Achieved

Commentary
Student response

Student 4 (PDF, 73KB)

For Achieved, the student needs to use each component of the statistical enquiry cycle to make comparisons.

This student’s evidence is a response to the TKI assessment resource ‘Sporting success’.

This student has posed an appropriate comparison question (1), selected and used appropriate displays (2), given summary statistics (3), discussed features of the distributions comparatively (4) and answered the comparison question (5).

To reach Merit, the student would need to justify the comments made about the features of the distributions, with reference to the visuals displays.

### Low Achieved

Commentary
Student response

Student 5 (PDF, 45KB)

For Achieved the student needs to use each component of the statistical enquiry cycle to make comparisons.

This student’s evidence is a response to the modified TKI assessment resource ‘Get Online’.

This student has posed an appropriate comparison question (1), selected and used appropriate displays (2), given summary statistics (3), discussed features of the distributions comparatively (4) and answered the investigative question (5).

For a more secure Achieved, the student would need to describe further features of the distributions, for example the spread, the overlap and the shape, and demonstrate a clearer understanding of the population.

### High Not Achieved

Commentary
Student response

Student 6 (PDF, 63KB)

For Achieved, the student needs to use each component of the statistical enquiry cycle to make comparisons.

This student’s evidence is a response to the modified TKI assessment resource ‘Sporting success’.

This student has posed a comparison question (1), selected and used appropriate displays (2), given summary statistics (3), compared the summary statistics (4) and answered the investigative question (5).

To reach Achieved, the student would need to relate the features of the distributions to the visual displays, and relate the question and answer to the population.