Mathematics - Level 3
AS90645 (3.5) Select and analyse continuous bi-variate data (Version 2)
These exemplars are based on data from two contexts.
The first involves measurements taken from a sample of mussels. Variables are the length (mm),
the width (mm), the thickness (mm), the mass of the shell only (g) and the mass of the mussel
without the shell (g).
The second involves data collected by a potato seed distributer from some of his clients. Variables
are yield (t/ha), amount of fertiliser applied (kg/ha), average daily amount of water applied (L)
over the growing season, average soil temperature (oC) over the growing season.
Student Exemplars at the Excellence - Merit boundary.
Student Response (assumptions)
When I got my relationship between the yield and the amount of fertiliser I had to assume that all
of the other variables stayed constant. This is not so because for example the data shows that the
amount of water that was applied also varies. To do it properly potatoes could be grown in the
same place so that the watering and temperature would be the same.
Student Response (limitations)
Predictions should be OK for amounts of fertiliser up to 25 t/ha because points are relatively close
to the regression line here. Between 25 and 30 t/ha points are more scattered and tend to be above
the line giving me less confidence in my predictions and they could be too low. But after this all
points are under the regression line. This means that predictions for amounts more than 30 t/ha
could be too high.
Student Response (usefulness)
Researchers working for the farm that the mussels came from would find the relationship between
mussel mass and length useful. For commercial production people would want to know how much
mussel mass they can get and so while mussels are growing they might want an idea of the mass.
But they have to open the mussel to get the mass and this means it could not be returned to the
water. So this way we can get an idea of mass by using the length equation.
Student Response (improvements)
y = 3E-10x 4.5059
R2 = 0.8912
Mussel mass
50
Mass(gm)
40
30
20
10
0
150
170
190
210
230
250
Length(mm)
270
290
310
330
Since the data appears to curve upwards I tried to use a power function as a regression model.
This fits the data better, particularly for the longer mussels. So any extrapolations I make should
be more accurate than with the linear model. But as the power function will continue to curve up I
still would not be that confident about extrapolations more than a little way out from the data and
there will a value that is not reasonable to be the mass of mussel.
Commentary
This provides evidence for Excellence because a correct assumption has been made and also is
referenced back to the analysis.
This provides evidence for Excellence because a limitation of the analysis has been identified and
the possible effect of the limitation has been discussed in context.
This provides evidence for Excellence. The possible use relates to the actual analysis and also is
reasonable in terms of the context of the investigation.
This provides evidence for Excellence. The limitation and corresponding improvement relate to the
analysis rather than the data.
Student Exemplars at the Excellence – Merit boundary.
Student Response (assumptions)
When investigating the potato data I have assumed that all other variables have been constant
Student Response (limitations)
I can be confident with my predictions when they are for values inside the data range because
interpolation is reliable but I am not confident with predictions when the amount of fertiliser is
greater than 37 t/ha. This is because I am extrapolating.
Student Response (usefulness)
The relationship between the mussel width and the length of the muscle would be useful to
fishermen because they could estimate the width by just measuring the length. The Ministry of
Fisheries could use these results to set quotas.
Student Response (improvements)
My investigation is limited because there were a small amount of data and so I could improve it by
taking a bigger sample. Also I could sample mussels from other parts of the country so the results
could be used more widely.
Commentary
This does not provide evidence for Excellence because, while it is an appropriate assumption, there
is no reference to the analysis that has been undertaken.
This does not provide evidence for Excellence because there is no reference to the actual analysis
to support any possible limitations in terms of extrapolation.
This does not provide evidence for Excellence. For the first comment it is not sensible to say that a
fisherman would use a measuring device to get the length and then use correlation to find the
width. For the second comment there is no justification for how the establishment of a
length/width relationship would help to set a quota.
This does not provide evidence for Excellence. The first suggested improvement is not at the level
which is expected for this standard. The second one does not relate to the actual analysis and
implies a completely different investigation.