A group of teachers were shown the graphs you see here. They made the following statements. Classify each of these by clicking on one of the three categories Correct, Unknown (the graph doesn't give us enough information) or Incorrect.

	Correct	Unknown	Incorrect
The school's median for Numeracy is a little higher than that for Reading
There is a greater diversity of the school's scores in Numeracy than in Reading
In the lower half of the school's Year 7 group the scores are a little more diverse in Reading than in Numeracy
The box-and-whisker plot indicates that Reading is the school's weakest area
Very few of the Example College students have scores in the top 25% of the state for Reading

Then click the Next button.

Statement One — Answer

The statement 'The school's median for Numeracy is a little higher than that for Reading' is Correct because the median (50th percentile) marker for Numeracy is a bit over 530, while that for Reading is a bit below 530. However for planning programs it is more important to compare the school with the state.

The school median is well below the state for Reading and a little below for Numeracy. This means that perhaps it may be more appropriate to have an additional focus on Reading rather than on Numeracy.

Statement Two — Answer

Whether the statement 'There is a greater diversity of the school's scores in Numeracy than in Reading' is correct or incorrect is Unknown, as the graph does not give us enough information.

It is true that the middle 50% (indicated by the red box) of Numeracy ranges between Band 5 and Band 8 whilst that for Reading ranges between Band 5 and Band 7.

A similar diversity is observed when comparing the middle 80% for each set of scores. However, since the extreme 10% at each end are not shown by the graph, and it is impossible to tell how spread out these outlying scores are – because they aren't shown in the box-and-whisker plot at all – it is unknown whether the statement is true overall.

Statement Three — Answer

Whether the statement 'In the lower half of the school's Year 7 group the students' scores are a little more diverse in Reading than in Numeracy' is correct or incorrect is Unknown, as the graph does not give us enough information.

All we know about the diversity of the scores of 'the lower half of the school's Year 7 group' is really from the 10th to the 50th percentiles, where Reading shows slightly more variation than Numeracy.

There could be 'clumping' together or a spreading out of the data within these regions – the box-and-whisker plot does not tell us. However, remember the lowest 10% of scores are not represented by the box-and-whisker plot. If you need to know this information, you would need to look at those individual students' results.

Statement Four — Answer

The statement 'The box-and-whisker plot indicates that Reading is the school's weakest area' is Correct.

In Reading, all 5 of the key markers – the median, and the 10th, 25th, 75th and 90th percentiles – are much lower than those for the state. This happened for no other NAPLAN test shown on this report.

Statement Five — Answer

The statement 'Very few of the Example College students have scores in the top 25% of the state for Reading' is Correct. Example College's 90th percentile is below the state's 75th percentile, so at most only 10% (or less) of the Example College students have scores that are located in the region of the state's top 25%. This allows for the possibility that none of the scores are in the state's top 25%.

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End of Tutorial