What Does the Graph Tell Us?

The box-and-whisker plot on the left shows the distribution of NAPLAN Numeracy results for the Year 7 students at Example College.

What does this graph tell us? Click Next to view seven statements made by teachers about this graph.

Classify the Statements

Classify each of the following statements by clicking on one of the three categories Correct, Unknown (the graph doesn't give us enough information) or Incorrect.

	Correct	Unknown	Incorrect
The middle 50% of students have scaled scores between about 460 and 630
Approximately half of the students have scores below 530
The lowest 10% of scores are below 460
This distribution for Numeracy is centred in Band 7
Most of the scores are between the 50th to 75th percentiles
Most of the students have scores which are above the 50th percentile
The Year 7 mean for Numeracy at Example College is low

Then click the Next button.

Statement One — Answer

The statement 'The middle 50% of students have scaled scores between about 460 and 630' is Correct because the 'box' of the box-and-whisker plot starts at the 25th percentile (about 460) and finishes at the 75th percentile (about 630).

Statement Two — Answer

Whether the statement 'Approximately half of the students have
scores below 530' is correct or incorrect is Unknown. Whilst the median is close to 530, it is clearly above it. The number of scores that are between the median and 530 is unknown (even though the visual space is small); it could be a very large or a very small proportion of the fixed 25% of scores represented by the lower portion of the red box. Therefore the graph does not give us enough information.

Statement Three — Answer

The statement 'The lowest 10% of scores are below 460' is Correct because the lower whisker of the box-and-whisker plot finishes at the 10th percentile (about 460).

Statement Four — Answer

The statement 'This distribution for Numeracy is centred in Band 7' is Correct. The centre of the distribution of the data is the median, shown by the line within the red box. This is within Band 7.

In addition to this, the graph shows that at least 90% of the College's students are above the National Minimum Standard.

Statement Five — Answer

The statement 'Most of the scores are between the 50th and 75th percentiles' is Incorrect.

The 50th and 75th percentiles are simply the start and finish of the third quarter of the ordered set of values; in other words, this part of the graph represents the test scores for only 25% of the class.

The fact that this is a larger portion of the red box simply means that these results are more spread out than, say those in the 25th to 50th percentile, etc.

Statement Six — Answer

The statement 'Most of the students have scores above the 50th percentile' is Incorrect. The midway marker for the ordered set of values is the median, or 50th percentile. Therefore half of the students have test scores above this marker, and the other half are below.

Statement Seven — Answer

Whether the statement 'The Year 7 mean for Numeracy at Example College is low' is correct or incorrect is Unknown. The mean of a set of data, or its average, is not indicated on a box-and-whisker plot. There is insufficient information from which to make a good estimate of the mean.

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End of Tutorial