Download Mathematics and Statistics 91037: Demonstrate understanding of

Mathematics and Statistics 91037: Demonstrate understanding of chance and data
Assessment Criteria
Achievement
Merit
Excellence
Demonstrate understanding of chance
Demonstrate understanding of chance
and data, justifying statements and
and data, showing statistical insight will
Demonstrate understanding of chance
findings will involve:
involve:
and data will involve using a range of
providing supporting evidence such as
integrating the statistical and contextual
appropriate concepts and terms to
summary statistics, probabilities, data
information and knowledge to show a
demonstrate an understanding of
values, trends or features of visual
deeper understanding
statistical literacy and probability.
displays
critical reflection on the validity of the
reference to the context and the
processes and conclusions given in
population.
contexts involving probability or statistics.
Evidence Statement
One
Expected coverage
Achievement
Merit
Excellence
(a) (i)
18/32
or equivalent
correctly deducing the
probability in any form.
(a) (ii)
8/32
or equivalent
correctly deducing the
probability in any form.
(a)
(iii)
11/24
or equivalent
(a)
(iv)
5/18
or equivalent
(b)
13/18*11/14 = 143/252
or equivalent
demonstrating
understanding of chance
by identifying the size of
the sample space denominator
demonstrating
understanding of chance
by identifying the size of
the sample space denominator
correctly deducing the
probability in any form.
correctly deducing the
probability in any form.
correctly deducing the
probability in any form.
correctly deducing the
probability in any form.
Two
a)
Expected coverage
e.g.
Hemi shows an increasing trend
in rentals during the week from
Thursday to Sunday only.
Jonno shows a steady increase
from Monday to Wednesday,
dropping off Thursday and
peaking on both Friday and
Sunday.
Achievement
b i)
Hemi in fact has a greater total
(21) than Jonno (17)
Valid comment made
b ii)
While Hemi does have a greater
total of DVD’s the graph gives no
information about money spent.
Valid comment made
Valid comment made
Title says “New Releases” so that
it could be implied all DVD’s cost
same amount and so
b iii)
e.g. If August is a representative
month then the claim could be
true.
However, sampling variability
alone could mean that it could be
the other way around in other
months.
Whether the flatmates watched
the movies together or
independently The hiring of
DVD’s might be an dependent
event as the two both watch
them.
Merit
Valid comment made
regarding title making a
valid comment on the
choice of classes
Valid comment made
Valid comment made with
justification
Valid comment made with
justification
Excellence
c)
Comments about data collection
e.g. Time of day?
Maybe rush hour was the reason
for the outlier.
How was rounding of times
carried out
What speed did the two flat-mates
travel?
Traffic lights/road works
Valid comment made with
justification
We have no knowledge as to the
timing (experiment) was carried
out except from graph of days.
Lurking variable could be day that
DVD hired. Johno and Hemi tend
to hire on different days/
Valid comment made with
insight
Comments about data display
e.g. No obvious difference in
graphs
Valid comment made
Comments about data analysis
e.g. Mean suggests that Hemi’s
route should be used as his mean
travelling time is lowest. Measure
of central tendency needs to be
more robust than simply the
mode.
using a measure of central
tendency to make a valid
conclusion
noticing that the mean will
have been affected by the
more wild guesses thus
raising the mean for
Johno’s mean time.
making an observation
about a measure of spread
but not relating it to the
conclusion
using a measure of spread
to make a valid conclusion
IQR suggests that Johno’s times
are more consistent (also seen in
the box and whisker graph).
Std. Deviation and range suggest
that the Hemi’s times are more
consistent (also seen in the
frequency graph).
Comment regarding
sampling variability
Making an informal
inference based on overlap
Comments about data analysis
(continued)
With samples of this size the
amount of overlap in the IQR’s
would mean that I would be
unable to claim that there is a
difference in travel times. This
could have happened by chance.
Three Expected coverage
a)
Total for
two
spinners
Expecte
d values
b)
of middle 50%
Comment regarding
sampling variability in
context of problem
Making an informal
inference based on overlap
of middle 50%
Achievement
9
10
11
150
80
10
Valid comment made with
insight
Merit
Excellence
correctly deducing the
probability in any form.
If the second spinner does have
two 6’s you could expect the
following
Total for
two
spinners
Expecte
d values
9
10
11
120
100
20
correctly deducing the
probability in any form
Too hard too call. Could be either
situation. Sample could have
happened by chance.
Need more data to be sure.
Sufficiency
Valid comment made with
insight
2a Q1 and 2a Q2
3m
2e