Internal assessment resource Mathematics and Statistics 1.10B v3 for Achievement Standard
91035
PAGE FOR TEACHER USE
This resource supports assessment against:
This resource:

Clarifies the requirements of the standard

Supports good assessment practice
 Should be subjected to the school’s usual assessment quality assurance process

Should be modified to make the context relevant to students in their school environment and ensure that submitted evidence is authentic
Date version published by
Ministry of Education
February 2015 Version 3
To support internal assessment from 2015
Quality assurance status These materials have been quality assured by NZQA.
NZQA Approved number A-A-02-2015-91035-02-4527
Authenticity of evidence Teachers must manage authenticity for any assessment from a public source, because students may have access to the assessment schedule or student exemplar material.
Using this assessment resource without modification may mean that students ’ work is not authentic. The teacher may need to change figures, measurements or data sources or set a different context or topic to be investigated or a different text to read or perform.
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Internal assessment resource Mathematics and Statistics 1.10B v3 for Achievement Standard
91035
PAGE FOR TEACHER USE
The following guidelines are designed to ensure that teachers can carry out a valid and consistent assessment using this internal assessment resource.
Teachers need to be very familiar with the outcome being assessed by Achievement
Standard Mathematics and Statistics 91035. The achievement criteria and the explanatory notes contain information, definitions, and requirements that are crucial when interpreting the standard and assessing students against it.
This activity involves students using the statistical enquiry cycle to make comparisons between groups in a population. The context for this resource is a student selected sample from the 2009 New Zealand Census At School multivariate data set.
This task could be adapted to use either the 2005 or 2007 New Zealand Census At
School surveys or the kiwi data population that are located within the data viewer. http://www.censusatschool.org.nz/2010/data-viewer
This activity requires at least two separate sessions. All work must be completed independently. In the first session, students should use approximately 20 minutes to review the variables and pose two comparison investigative questions. While two questions are asked for, only one is needed for the investigation. Not all combinations of variables are suitable for investigation, for example, height compared by reaction time. The variables suggested for this activity support eight investigations:
 height compared by gender or age
 arm span compared by gender or age
 right foot length compared by gender or age
 reaction time compared by gender or age.
Other combinations are unsuitable or trivial. This achievement standard requires students to compare a numerical variable across categories; a comparison of category variables is not appropriate. In other words, one of the variables investigated must be continuous and the other a category variable, for example, height and gender. It is not appropriate to investigate a relationship situation for this task.
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Internal assessment resource Mathematics and Statistics 1.10B v3 for Achievement Standard
91035
PAGE FOR TEACHER USE
Check students’ investigative questions, and, if required, provide time for students to correct or improve their questions, before beginning the second session. If they are unable to improve their questions so that they have at least one suitable investigative question, give feedback of a general nature indicating which of the question criteria have not been met; do not provide the question. Where more than minimal feedback is needed, the student is not ready for assessment against this standard.
The second (and subsequent) sessions are for students to carry out the analysis and write conclusions. Any technology is allowed for the analysis.
Students need a variable list for the Census At School data including the survey questions that were asked. Included with this assessment activity is an abridged version of the 2009 variables (Student Resource A).
For the full variable list: http://www.censusatschool.org.nz/2009/variables/.
For 2009 questions: http://www.censusatschool.org.nz/2009/questions/.
This activity requires students to have access to the online Census At School data viewer, http://www.censusatschool.org.nz/2010/data-viewer/ and to be familiar with its use. Provide students with the facility to print from the Census At School site.
You may wish to give students a template to assist them in posing investigative questions, for example:
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Looking at the data, what are you curious about? Complete the statement
“I wonder …”
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Write down the variables that you are investigating.
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What are the groups you are comparing?
The 2009 New Zealand Census at School can be found at: http://www.censusatschool.org.nz
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Internal assessment resource Mathematics and Statistics 1.10B v3 for Achievement Standard
91035
PAGE FOR STUDENT USE
Achievement
Investigate a given multivariate data set using the statistical enquiry cycle.
Achievement with Merit
Investigate a given multivariate data set using the statistical enquiry cycle, with justification.
Achievement with
Excellence
Investigate a given multivariate data set using the statistical enquiry cycle, with statistical insight.
This activity requires you to undertake an investigation using the 2009 New Zealand
Census At School database. First, you will pose two investigative questions. Then you will take a sample using the Census At School online data viewer, analyse the sample, and form a conclusion for one of your investigative questions.
This activity is to be completed independently.
You will be assessed on the quality of your discussion and reasoning, and how well you link this to the context.
As you carry out this task, you will use the statistical enquiry cycle (Problem, Plan,
Data, Analysis and Conclusion).
Pose two investigative questions about students from the 2009 New Zealand Census
At School database using the variables described in Student Resource A. Your investigative questions must be comparison questions. (A suitable comparison investigative question is one that reflects the population, has a clear variable to investigate, compares the values of a continuous variable across different categories, and can be answered with the data.)
For each question state the variable you are investigating and the groups you are comparing.
Now choose one of your two questions to complete the investigation.
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Internal assessment resource Mathematics and Statistics 1.10B v3 for Achievement Standard
91035
PAGE FOR STUDENT USE
Use the Census At School online data viewer, http://www.censusatschool.org.nz/2010/data-viewer , to select a sample of 30 from each of your groups.
Managed through New Zealand Census At School survey team.
Draw at least two appropriate graphs that show different features of the data in relation to your investigative question.
Give appropriate summary statistics.
Describe features of the distributions comparatively, for example, shape, middle
50%, shift, overlap, spread, unusual or interesting features.
Write a conclusion summarising your findings. The conclusion needs to include an informal inference in response to your investigative question and be supported with relevant evidence.
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Internal assessment resource Mathematics and Statistics 1.10B v3 for Achievement Standard
91035
PAGE FOR STUDENT USE
In the 2009 New Zealand Census At School survey students answered 35 questions in an online survey.
A selection of variables from the survey is listed below, with the survey question used.
Variable Survey question gender Are you: boy/girl? age (in years) How old are you? year What year level are you? height (in cm) How tall are you without your shoes on? Answer to the nearest centimetre. right foot length
(in cm) arm span (in cm) reaction time
(in seconds)
What is your right foot length, without a shoe? Answer to the nearest centimetre.
What is your arm span? Answer to the nearest centimetre. (Open arms wide, measure distance from tip of right hand middle finger to tip of left hand middle finger.)
How fast is your reaction time? Click on the green button. When it turns red, click it as fast as you can.
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Internal assessment resource Mathematics and Statistics 1.10B v3 for Achievement Standard 91035
PAGE FOR TEACHER USE
Teacher note: You will need to adapt this assessment schedule to include examples of the types of responses that can be expected.
Evidence/Judgements for Achievement
The student shows evidence of investigating a given multivariate data set using each component of the statistical enquiry cycle.
The student:
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poses an appropriate comparison question
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draws graph(s) and gives summary statistic(s) that allow features of the distributions to be described in relation to the question

writes statements that describe comparative features of the distributions in context. (At least two statements, describing different features, are expected.)

answers the comparison question in the context of the investigation or makes a correct comparison using an informal inference about the population.
Example of possible evidence:
The student poses an appropriate comparison question.
Do the reaction times for year 11 boys tend to be faster than year 11 girls in the 2009 Census At
School database?
The student selects the samples of boys and girls and produces at least one graph and summary statistics.
The student describes at least two comparative
Evidence/Judgments for Achievement with
Merit
The student shows evidence of investigating a given multivariate data set using each component of the statistical enquiry cycle, with justification.
The student:

poses an appropriate comparison question

draws graph(s) and gives summary statistics that allow features of the distributions to be described in relation to the question

writes statements with evidence that describe comparative features of the distributions in context. (At least two statements describing different features are expected.)

makes a correct informal inference about the population from the sample data that shows an understanding of sampling variability or of the context

answers the comparison question, with at least one statement of supporting evidence.
Example of possible evidence:
The student poses an appropriate comparison question.
Do the reaction times for year 11 boys tend to be faster than year 11 girls in the 2009 Census At
School database?
The student selects the samples of year 11 boys and year 11 girls and produces at least one graph
Evidence/Judgements for Achievement with
Excellence
The student shows evidence of investigating a given multivariate data set using each component of the statistical enquiry cycle, with statistical insight.
The student:

poses an appropriate comparison question

draws graphs and gives summary statistics that allow features of the distributions to be described in relation to the question. (At least two different graphs showing different features are expected.)

writes statements with evidence that describe key comparative features of the distributions in context. (At least three statements describing different features are expected; key features include middle 50%, shift and overlap, shape, spread, unusual or interesting features.)

makes a correct informal inference about the population from the sample data that shows an understanding of sampling variability and of the context

answers the comparison question with reference to the population and key supporting evidence summarised in context. (What the statistical basis for the claim is and the effect of sampling variability or does the claim make sense considering the actual situation is expected.)
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Internal assessment resource Mathematics and Statistics 1.10B v3 for Achievement Standard 91035
PAGE FOR TEACHER USE features in context.
The reaction times for both boys and girls are tightly bunched around the 0.4 second mark.
Both the boys and girls have a few reaction times that are a lot higher than the others.
The student answers the comparison question in context.
The box for the boys’ reaction times is slightly lower than the box for the girls’ reaction times, so boys tend to react a bit faster. and summary statistics.
Note: The summary statistics may only be evident in the description. Not all are needed, sufficient to support the description. They could be read off the graph, or given by statistical software.
The student describes, with evidence, at least two comparative features in context
The reaction times for boys and girls are tightly bunched between 0.3 seconds and 0.5 seconds.
The median reaction time for boys (0.36 seconds) is slightly lower than the girls (0.42 seconds) and is outside the overlap of the boxes containing the middle 50% of the times.
The student makes a correct informal inference, which shows an understanding of sampling variability or of the context and answers, with supporting evidence, the comparison question.
I would claim that the reaction times for year 11 boys tend to be faster than the reaction times for year 11 girls in the Census At School database. I would make this claim as the median for boys’ reaction times is outside the overlap of the boxes.
This makes sense to me, because in sports like race car driving and sprinting, where reaction times are very important, male athletes seem to do better than females.
Example of possible evidence:
The student poses an appropriate comparison question.
Do the reaction times for year 11 boys tend to be faster than year 11 girls in the 2009 Census At
School database?
The student selects the samples of year 11 boys and year 11 girls and produces both a dot plot and a box plot and summary statistics.
Note: The summary statistics may only be evident in the description. Not all are needed, sufficient to support the description. They could be read off the graph, or given by statistical software.
The student reflects on at least three features of the distribution comparatively.
The reaction times for boys and girls are tightly bunched between 0.3 seconds and 0.5 seconds.
Both the boys and girls reaction times are skewed to the right. For the boys the skew is because of the three reaction times, which are much longer than the rest, which are tightly bunched between
0.3 seconds and 0.5 seconds. The boys’ reaction times have a maximum of 3.93 seconds and the girls’ reaction times a maximum of 2.98 seconds.
The middle 50% of reaction times for boys
(0.35 – 0.46 seconds) have a similar spread to the girls (0.41 – 0.5 seconds). The middle 50% of the girls’ reaction times is shifted further to the right so they are slower than the middle 50% of boy s’ reaction times.
The median reaction time for boys (0.36 seconds) is slightly lower than the girls (0.42 seconds) and is outside the overlap of the boxes containing the middle 50% of the reaction times.
The student makes a correct informal inference about the population from the sample data, which
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Internal assessment resource Mathematics and Statistics 1.10B v3 for Achievement Standard 91035
PAGE FOR TEACHER USE shows an understanding of sampling variability and of the context and answers the comparison question with reference to the population and key supporting evidence summarised in context.
Considers other explanations for the findings.
I would claim that year 11 boys’ reaction times tend to be faster than year 11 girls’ reaction times in the 2009 Census At School database. This makes sense because a lot of the boys I know are into play stations and video games and these require quick reaction times to score high points.
This claim is based on the fact that the median for boys’ reaction times is outside the overlap of the middle 50% of reactions times and the middle 50% of times for boys is further down the scale than the girls’ middle 50%. This evidence suggests that what I see in my samples is what is happening back in the 2009 Census At School database for all year 11 boys and girls.
If I was to repeat this sampling process I would expect to see year 11 boys’ reactions times tending to be faster than year 11 girls’ reaction times again, as the distance between the medians is more than 1/3 of the overall visual spread and this is sufficient to make a claim for samples of about 30.
Final grades will be decided using professional judgement based on a holistic examination of the evidence provided against the criteria in the
Achievement Standard.
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