# Mathematics and Statistics - annotated exemplar Level 3 AS91580

## Investigate time series data (3.8)

 Read the STANDARD TKI Mathematics and Statistics Assessment Resources Download all these exemplars and commentary (PDF, 2.7MB)

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.

There is new student evidence for Low Excellence, Low Merit, High Achieved and High Not Achieved.

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

### Low Excellence

Commentary
Student work extract

Student 1 (PDF, 570KB)

For Excellence, the student needs to investigate time series data, with statistical insight.

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

This evidence is from a student’s response to the TKI task ‘Food for thought’.

The student has researched the context, used this to develop a clear purpose for the investigation (1), and has selected and used appropriate displays throughout their response.

There is evidence of statistical and contextual knowledge from appropriate research being integrated in the discussion of features through the consideration of population and takeaway sales as relevant variables (2).

The appropriateness of the model used to make forecasts has been discussed with an evaluation of the adequacy of the model and discussion of the reliability of the calculated seasonal effects (3).

This extract is from a student response which also included the student comparing actual values with predicted values and prediction intervals to confirm the robustness of the fitted model. The student also communicated findings in a conclusion to an appropriate level for the award of Excellence.

For a more secure Excellence the student would need to develop their comments about the model. For example, explaining the unusual residuals by linking their comments more closely to contextual knowledge gained from research. Interpreting the prediction intervals would also show a deeper understanding of the adequacy of the model.

### High Merit

Commentary
Student work extract

Student 2 (PDF, 927KB)

For Merit, the student needs to investigate time series 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 ‘Polar ice’.

The student has researched the context and used this to develop a purpose for the investigation relevant to the variable being investigated (1). The student has selected and used appropriate displays throughout their response.

The student has investigated time series data by linking the findings to the context throughout the response. For example, when discussing features, they have used evidence to support statements in describing the trend (1), the feature of seasonal variation (2), the appropriateness of the model (3) and the reliability of the forecast (4).

In their conclusion, the student has linked the comments made back to the context and the purpose of their investigation (5).

To reach Excellence, the student would need to provide a more detailed summary in the conclusion and more clearly integrate statistical and contextual knowledge derived from research. For example, the student could link their statements to supporting or contradicting evidence found in the research.

### Low Merit

Commentary
Student work extract

Student 3 (PDF, 371KB)

For Merit, the student needs to investigate time series 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 ‘Food for thought’.

The student has provided evidence of some research related to the purpose of the investigation and the variable being investigated (1). The student has selected and used appropriate displays throughout their response.

The student has identified the change in the smoothed data and linked this to evidence shown in the graph (2). Descriptions of the seasonal pattern have been accurately related to the context (3).

They have also used an appropriate model to make a forecast which has been given in context and appropriately rounded (4). A comment on the accuracy of the forecast has been given in the conclusion (5).

For a more secure Merit, the comment on the accuracy of the forecast needs to be developed. For example, the student could consider how changes in the smoothed data towards the end of the graph would potentially have an effect on the estimated value of the forecast.

The student could also link their comments made in their conclusion back to the purpose for their investigation.

### High Achieved

Commentary
Student work extract

Student 4 (PDF, 208KB)

For Achieved, the student needs to show evidence of using each component of the statistical enquiry cycle to investigate time series data.

This involves: using existing data sets, selecting a variable to investigate, selecting and using appropriate display(s), identifying features in the data and relating this to the context, finding an appropriate model, using the model to make a forecast and communicating findings in a conclusion.

This evidence is from a student’s response to the TKI task ‘Food for thought’.

There is evidence of some research related to the purpose of the investigation (1).

The student has selected a variable to investigate and has used software to select and use appropriate displays and find an appropriate model (2).

Features of the data have been identified with descriptions of the trend and seasonal pattern, and the student has accurately related these to the context. A decreasing ramp in the data between 2008 and 2009 has been identified as a feature in the data (3).

The model has also been used to make a forecast (4) and a conclusion (5).

To reach Merit, the student needs to provide more evidence of linking the findings to the context and referring to evidence from the displays throughout the response. For example, when making a comment on the accuracy of the forecasts.

The link of the forecast to the context also needs to refer to the amount of money spent in supermarket and grocery stores, rather than how many sales there will be.

### Low Achieved

Commentary
Student work extract

Student 5 (PDF, 492KB)

For Achieved, the student needs to show evidence of using each component of the statistical enquiry cycle to investigate time series data.

This involves: using existing data sets, selecting a variable to investigate, selecting and using appropriate display(s), identifying features in the data and relating this to the context, finding an appropriate model, using the model to make a forecast and communicating findings in a conclusion.

This evidence is from a student’s response to the TKI task ‘Polar ice’.

The student has selected an appropriate variable to investigate (1), selected and used appropriate displays (2), identified features (trend and seasonal variation) in the data and related them to the context (3), found an appropriate model (4), used the model to make a forecast (5) and communicated findings in a conclusion (6).

For a more secure Achieved, there needs to be a better overall understanding of the context. In the description of the trend, the student needs to refer to the decrease in the mean area of sea ice in the Arctic as an ‘average’ effect.

The student would also need to provide evidence of researching the context prior to selecting the variable they will investigate.

### High Not Achieved

Commentary
Student work extract

Student 6 (PDF, 282KB)

For Achieved, the student needs to show evidence of using each component of the statistical enquiry cycle to investigate time series data.

This involves: using existing data sets, selecting a variable to investigate, selecting and using appropriate display(s), identifying features in the data and relating this to the context, finding an appropriate model, using the model to make a forecast and communicating findings in a conclusion.

This evidence is from a student’s response to the TKI task ‘Food for thought’.

The student has selected an appropriate variable to investigate (1), selected and used an appropriate display, and found an appropriate model (2). The student has also identified a feature in the data by describing the trend in context (3).

To reach Achieved, evidence for identifying features in the data would need to include the seasonal pattern. The student would also need to more clearly relate the description of the trend to the context by including the dates.

In addition, the student needs to provide evidence of researching the context prior to selecting the variable they will investigate.