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Data Interpretation Insights

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Data Interpretation Insights

Use the data displays to answer each question. Give evidence from the data where asked. Remember that an association does not, by itself, show that one variable causes another.

A. Study habits and assessment results

A fictional survey of ten Year 11 students in Aotearoa New Zealand recorded their usual weekly independent maths study time and their score on a common assessment.

Study time (hours per week)

Assessment score (%)

1.Describe the direction and strength of the overall association between weekly study time and assessment score. Refer to the pattern in the paired data.

2.One student studied 9 hours and scored 45%. Explain why this point might be considered unusual in the context of the overall pattern, and give one sensible reason for checking it before drawing a conclusion.

3.A student studying 5.5 hours asks you to estimate their score from this survey. Give a reasonable estimate and explain why it is an estimate rather than a guaranteed result.

4.Which conclusion is best supported by this small survey?

Studying more hours causes every student to achieve a higher score.
In this survey, higher study times generally occurred alongside higher scores, but other factors may also matter.
Study time and assessment score have no association.
A student who studies 10 hours is guaranteed to score 88%.

B. Comparing regional score distributions

A second fictional data summary compares assessment scores from two groups of students. The summary statistics are supplied so you can focus on interpreting what the distributions suggest.

Group

Median score (%)

Interquartile range (IQR)

Auckland sample

Canterbury sample

5.Compare the typical score and the spread of scores for the two samples. Use the median and IQR values in your explanation.

6.Can the summaries prove that every Auckland student scored higher than every Canterbury student? Explain your answer.

7.A news post says, “Auckland students are better at maths than Canterbury students,” based only on these summaries. Identify one important limitation that should be mentioned before making this claim.

C. Check the claim

A study announcement reports that a group’s mean score increased from 50% to 55%. The announcement calls this a “10% increase in achievement”.

8.Check the announcement’s calculation. What is the increase in percentage points, and what is the relative percentage increase from the original mean?

9.The announcement gives only the two means. Name two other pieces of information that would help readers judge whether the change is meaningful and how reliable the comparison is.