Repeated Random Sampling in Year 5

Figures & data

Figure 1. Questions from the ABS CensusAtSchool questionnaire <www.abs.gov.au/censusatschool>.

Figure 2. Example of how data were collected from the ABS CensusAtSchool “population.”

Figure 3. Example of a table recording percentages from random samples in a student Workbook.

Figure 4. Example of file created to code predictions (vertical labeled lines) for one student.

Figure 5. Example of plots satisfying the codes for predictions.

Table 1. Rubric for written responses to questions.

Question	Step	Description
Q1 Why did you choose these percentages?	0	No mathematical reason, e.g., “guessed,” “looking at the table”
	1	Partial explanation without detail or inconsistent with the Prediction Level
	2	Valid technique such as lots of, most, most common, middle, or average with Level 2 on Prediction
	3	Valid technique such as lots of, most, most common, middle, or average with Level 3 on Prediction
Q2 How close were your predictions of the population percentages? [Students had recorded the population values in their workbooks.]	0	No response
	1	Qualitative description
	2	Answer includes actual differences
Q3 Why do you think this was?	0	No response or guess
	1	Acknowledges poor strategy, “bad luck,” no acknowledgement of a statistical method
	2	Acknowledges use of statistical strategy

Figure 6. Distribution of mean codes for prediction (n = 87), highlighted by prediction levels.

Figure 7. Examples of prediction levels for four different mean values of codes.

Figure 8. Example of coding of the highest prediction level.

Figure 9. Relationship of prediction level and explanation of reasoning.

Figure 10. Two ways of viewing the same data from nine random samples.