# 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, 625KB)

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 May 2019.

There is new student evidence for the Low Excellence and Low Merit exemplars for this standard.

The annotations for Low Excellence, High Merit, Low Merit and High Achieved have been altered to better illustrate the requirements of the standard.

### Low Excellence

Commentary
Student response

Student 1 (PDF, 164KB)

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 comes from the TKI assessment resource ‘Sporting success’.

The student has posed an appropriate comparison question (1), selected and used appropriate displays (2), given summary statistics (3), discussed features of distributions comparatively (4), and communicated an informal inference in their conclusion (5).

The student has provided evidence of statistical insight throughout the statistical enquiry cycle, and demonstrated statistical knowledge in the comment about the use of 0.41 for DBM/OVS (6). The student has also started to reflect on the process (7).

For a more secure Excellence, the student could strengthen the reflection on the process and consider other explanations. For example, the student could consider the current world rankings of the teams. They could also strengthen the depth of the contextual discussion.

### High Merit

Commentary
Student response

Student 2 (PDF, 146KB)

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 the population and making supporting statements which refer to evidence such as summary statistics, data values, trends or features of visual displays.

The student has posed an appropriate comparison question (1), selected and used appropriate displays (2), given summary statistics (3), discussed features of distributions comparatively (4), and communicated an informal inference in their conclusion (5).

The student has provided justification for comments made by referring to supporting evidence. This is shown in the student’s discussion of the sample distributions and when making an informal inference (6).

The student has also justified their call through the correct use of the DBM/OVS ratio (7), and started to integrate statistical and contextual knowledge in the response by linking their findings to a local paper article about trout size (8).

To reach Excellence, the student would need to integrate the comments made with contextual knowledge throughout the response, and link the critical value of 0.2 to the sample sizes (close to 100).

### Low Merit

Commentary
Student response

Student 3 (PDF, 139KB)

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 the population and making supporting statements which refer to evidence such as summary statistics, data values, trends or features of visual displays.

This student’s evidence comes from the TKI assessment resource ‘Census At School’.

The student has posed an appropriate comparison question (1), selected and used appropriate displays (2), given summary statistics (3), discussed features of distributions comparatively (4), and communicated an informal inference in their conclusion (5).

In the conclusion, the call is justified by considering the position of the sample medians relative to the boxes of the other group, which is appropriate for sample sizes close to 30 (6).

When discussing sample distributions, the student has provided justification for comments made, for example by referring to the visual displays of data (7).

For a more secure Merit, the student would need to strengthen their discussion of the features of the distributions, for example discussing and justifying other features such as the overlap of the middle 50%.

The student could also strengthen the links to the context by ensuring, throughout the response, that the variable is identified as the number of text messages per day.

### High Achieved

Commentary
Student response

Student 4 (PDF, 183KB)

For Achieved, the student needs to investigate a given multivariate data set using the statistical enquiry cycle.

This involves using each component of the statistical enquiry cycle to make comparisons.

This student’s evidence comes from the TKI assessment resource ‘Sporting success’.

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

To reach Merit, the student needs to provide a clearer discussion of the features of the sample distributions, and justify their comments by referring to evidence in the visual displays.

The student would also need to show a clearer understanding about the variable being investigated (points scored in test matches).

### Low Achieved

Commentary
Student response

Student 5 (PDF, 123KB)

For Achieved, the student needs to investigate a given multivariate data set using the statistical enquiry cycle.

This involves using each component of the statistical enquiry cycle to make comparisons.

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

For a more secure Achieved, the student would need to provide a clearer understanding of the population the investigation is about. The student also needs to strengthen the comparative discussion of the features of the distributions, for example by discussing other features such as the spread and the shape.

### High Not Achieved

Commentary
Student response

Student 6 (PDF, 75KB)

For Achieved, the student needs to investigate a given multivariate data set using the statistical enquiry cycle.

This involves using each component of the statistical enquiry cycle to make comparisons.

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

To reach Achieved, the student would need to use appropriate evidence to make the call for sample sizes close to 100, and discuss features of the distributions comparatively.