# Mathematics - annotated exemplars level 1 AS91036 (Resource A)

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

 Read the STANDARD See EXEMPLAR B for this standard TKI Mathematics and Statistics Assessment Resources Download all these exemplars and commentary (PDF, 895KB)

### Exemplar 1:  Low Excellence

CommentaryStudent response
 1 Plan includes the relationship question. Variables have been determined and possible sources of variation have been identified and managed. 2 Data has been gathered. 3 Appropriate display has been presented. 4 The conclusion describes both the strength and direction of the relationship and also gives supporting reasons. This, and comments about the conclusion being ‘sensible’ show that the process has been reflected upon and that statistical and contextual knowledge has been integrated. The description of the strength lacks complete accuracy with the use of words like ‘fairly strong’, ‘pretty close’ and ‘tailing off’ and this is the reason for the classification of Low Excellence.
 Student 1 page 1 (JPG, 210KB)

### Exemplar 2:  High Merit

CommentaryStudent response
 5 Plan includes the relationship question. Variables have been determined and possible sources of variation have been identified and managed. 6 Data has been gathered. 7 Appropriate display has been presented. 8 The relationship has been described in context. 9 The conclusion contains two supporting comments. The first relates to the slope of the trend line and the second establishes a percentage bounce, providing justification and clear supporting statements. This is the reason for the classification of High Merit. 10 The student has not demonstrated statistical insight which is the requirement for Excellence because the strength of the relationship has not been discussed.
 Student 2 page 1 (JPG, 164KB) Student 2 page 2 (JPG, 127KB)

### Exemplar 3:  Low Merit

CommentaryStudent response
 11 Plan includes the relationship question. Variables have been determined and possible sources of variation have been identified and managed. 12 Data has been gathered. 13 Appropriate display has been presented. 14 The relationship has been described in context. 15 Merit requires two comments which support the conclusion. The comment about the lack of a strong pattern supports the conclusion that there is not a clear relationship but ‘strong pattern’ is not particularly clear and this is the reason for the classification of Low Merit. The second comment about a possible linear relationship is supported by the comment about the slope of the trend line. For Excellence statistical insight would require more depth in terms of reflecting about the process, the comment about the ‘unusual point’ lacks context and does not discuss possible affects of the point on the process.
 Student 3 page 1 (JPG, 139KB) Student 3 page 2 (JPG, 96KB)

### Exemplar 4:  High Achieved

CommentaryStudent response
 16 Plan includes the relationship question. Variables have been determined and possible sources of variation have been identified and managed. 17 Data has been gathered. 18 Appropriate display has been presented. 19 The relationship has been described in context. 20 The classification of High Achieved is because there is one supporting comment (about the slope of the trend line) but two comments are needed for Merit. There is no contextual justification which refers to the scatter graph to support the ‘strongly related’ comment. The ‘clusters’ are not identified, nor are they obvious on the scatter graph.
 Student 4 page 1 (JPG, 233KB) Student 4 page 2 (JPG, 123KB)

### Exemplar 5:  Low Achieved

CommentaryStudent response
 21 Plan includes the relationship question. Variables have been determined and possible sources of variation have been identified and managed. 22 Evidence of data gathering was not included with this script. It is assumed that the assessor had evidence of this and that the graph is consistent with the data. 23 Appropriate display has been presented. 24 The relationship has been described and the description includes a link to the context. 25 The classification of Low Achieved is because the contextual aspect of the description is implied as much as stated. Merit would require two statements which support the description and comments relating to both the ‘cluster’ and the ‘outliers’ are not supported by the appearance of the scatter graph.
 Student 5 page 1 (JPG, 101KB)

### Exemplar 6:  High Not Achieved

CommentaryStudent response
 26 Plan includes the relationship question. Variables have been determined and possible sources of variation have been identified and managed. 27 Evidence of data gathering was not included with this script. It is assumed that the assessor had evidence of this and that the graph is consistent with the data 28 Appropriate display has been presented. 29 The conclusion does not use the context of the investigation. Later comments lack statistical accuracy and do not communicate the relationship. 30 The classification of High Not Achieved is because the relationship has not been communicated well enough. To be at Achieved level the context would have to be included in the description; for example ’The increasing slope of the trend line means that Year 11 boys who jump further horizontally from their right foot also tend to jump further from their left foot’.
 Student 6 page 1 (JPG, 202KB)