Purpose
Achievement Criteria
Explanatory Note 1
Explore data using a statistical enquiry process involves:
- explaining different sources of variation in the data collection process
- presenting the data using at least one appropriate visualisation
- describing features of the data in context with reference to at least one appropriate visualisation.
Explore data using a statistical enquiry process with statistical justification involves:
- connecting ideas within the statistical enquiry process to complete an investigation
- justifying features of the data in context, using at least one appropriate visualisation and measure.
Explore data using a statistical enquiry process with statistical insight involves:
- incorporating statistical and contextual knowledge in the completed investigation, including reflecting on the statistical enquiry process.
Explanatory Note 2
Statistical enquiry process means the statistical enquiry cycle or a similar process for investigating statistics or probability.
The statistical enquiry process can follow one of four styles of investigation:
- comparison (numerical comparison of two or more groups)
- relationship (between two numerical variables)
- time series
- experimental probabilities (involving events with at least two stages).
Explanatory Note 3
Data collection process refers to the collation of suitable data sets of sufficient size. This includes:
- generating data through surveys or experiments using physical or digital methods, or sourcing from existing data
- selecting continuous data or discrete data values with a sufficient range of values to allow for analysis.
Shared Explanatory Note
Refer to the NCEA glossary for Māori, Pacific, and further subject-specific terms and concepts.
This achievement standard is derived from the Mathematics and Statistics Learning Area at Level 6 of The New Zealand Curriculum: Learning Media, Ministry of Education, 2007.
Conditions of Assessment
Assessor involvement during the assessment event is limited to providing guidance on a student’s plan for their investigation, ensuring that any collected or sourced data allows students to explain different sources of variation. Assessors will provide guidance to students on the selection of appropriate data sets, including the sample size. Assessors can provide a milestone check which offers enough guidance to keep a student on track but should not compromise the authenticity of student work. Guidance or feedback should avoid correction of specific detail.
At the start of the assessment event, students are able to choose the direction of their own investigation, including investigative question or statement, with assessor approval. Assessors must ensure an appropriately worded investigative question or statement is used. Assessors may correct the wording, or provide an appropriately worded investigative question or statement. Assessors will identify the population for any collected or sourced data.
Students may use appropriate technology and resources.
Students may work in groups to plan and source data but must work individually on all other stages of this Standard.
Evidence for all parts of this assessment can be in te reo Māori, English, or New Zealand Sign Language.
Unpacking the Standard
Examples of expected student responses for this Achievement Standard can be found at the bottom of the page.
Examples of expected student responses for this Achievement Standard can be found at the bottom of the page.
Mātauranga Māori constitutes concepts and principles that are richly detailed, complex, and fundamental to Māoridom. It is important to remember that the practice of these are wider and more varied than their use within the proposed NCEA Achievement Standards and supporting documentation.
We also recognise that the cultures, languages, and identities of the Pacific Islands are diverse, varied, and unique. Therefore the Pacific concepts, contexts, and principles that have been incorporated within NCEA Achievement Standards may have wide-ranging understandings and applications across and within the diversity of Pacific communities. It is not our intention to define what these concepts mean but rather offer some ways that they could be understood and applied within different subjects that kaiako and students alike can explore.
Mātauranga Māori constitutes concepts and principles that are richly detailed, complex, and fundamental to Māoridom. It is important to remember that the practice of these are wider and more varied than their use within the proposed NCEA Achievement Standards and supporting documentation.
We also recognise that the cultures, languages, and identities of the Pacific Islands are diverse, varied, and unique. Therefore the Pacific concepts, contexts, and principles that have been incorporated within NCEA Achievement Standards may have wide-ranging understandings and applications across and within the diversity of Pacific communities. It is not our intention to define what these concepts mean but rather offer some ways that they could be understood and applied within different subjects that kaiako and students alike can explore.
The intent of the standard
The purpose of this Achievement Standard is to enable ākonga to show their capabilities when exploring data, following an established statistical enquiry process.
Ākonga will use a statistical enquiry process to source data and carry out an investigation. For Achievement, there is greater emphasis on how data is sourced or collected, presented, and analysed. For higher levels of achievement, ākonga will provide evidence across the chosen enquiry process.
It is intended that ākonga will have the opportunity to explore the context before beginning their independent work. This could include brainstorming in groups or with the whole class, with kaiako support, to gain a greater understanding of potential purposes behind an investigation.
The intent of the Achievement Standard is to complete an investigation using a statistical enquiry process. Some end points are complex or difficult to define. Ākonga should present evidence for a completed enquiry process for higher levels of achievement.
The following sections show further details for each of the four different styles of investigation.
Relationship investigation
The intent of a relationship investigation is to collect or source data and describe any visible trend including direction and strength, as well as groups and unusual values. Ākonga should relate the features that they describe closely to the context. It is not appropriate to refer to x and y.
Relationship investigations are useful for making predictions. A completed investigation needs to include a prediction. All predictions made should be informal. Predictions could be made using substitution into a trend line formula or by visual inspection of the graph. Regression analysis lies outside the scope of this Achievement Standard.
Features of the data may include:
- direction and strength of relationship
- clusters
- unusual or interesting data points
- patterns.
Comparison investigation
The intent of a comparison investigation is to collect or source data, describe features comparatively, and make an informal sample to population inference. When using a sample with between 20 and 40 in each group, ākonga will use the three-quarters/half rule to make a call where it is clear, and visually use the distance between medians as proportion of “overall visible spread” where a call is not clear. When using a sample with 100 or 1000 in each group, they will visually use the distance between medians as proportion of “overall visible spread” to make a call. The following is a link that provides support related to making a call:
Guidelines for “How to make the call” (censusatschool.org.nz).
For samples with uneven group sizes, the size of the smaller group will determine the method for making a call. Students are expected to demonstrate the difference between a sample and a population.
Dot plots, stem and leaf graphs, or histograms on their own do not provide sufficient evidence for discussing features. They can be used as supporting evidence in conjunction with a box and whisker graph.
When sourcing data from digital or readily available data sets, samples of size 100 or 1000 per category are recommended.
Features of the data may include:
- centre
- spread
- shape
- shift and overlap of two groups
- clusters
- unusual or interesting data points.
Time series investigation
The intent of a time series investigation is to collect or source data and describe any trends, seasonality/cycles, patterns, variation, and unusual values. Time series investigations are useful for making future forecasts. A completed investigation needs to include a forecast. All forecasts should be informal. Forecasts could be made using a visual inspection of the graph. Formal long-term trend line analysis lies outside the scope of this Achievement Standard. As part of their investigation ākonga may reason that a forecast is not useful. For higher levels of achievement this should be with justification, with non-trivial explanations and extended abstract thinking at the highest levels of achievement.
Features of the data may include:
- trend of time series
- unusual or interesting data points, spikes, or troughs
- seasonality, cycles
- patterns.
Experimental probability investigation
The intent of an experimental probability investigation is to conduct an experiment to collect data and describe observed probabilities in context. In some situations, with theoretical probabilities it may be appropriate to use simple simulations. Simulations could also be run with collected data where a theoretical model does not exist. An experiment using a tool with a simple outcome (dice, spinner) needs to use digital simulation to be at the right level.
Features of the data may include:
- clusters
- unusual or interesting data points
- centre
- spread
- shape
- patterns.
Making reliable judgements
To explore data effectively requires sufficient data — each style of investigation has different minimum recommendations:
- Relationship — 30 pairs of data.
- Comparison — 30 pieces of data from each category explored.
- Time series — 5 complete cycles.
- Experimental probability — 30 trials.
Using a statistical enquiry process usually requires ākonga to work through a set of steps. Evidence submitted should be marked holistically against a whole statistical enquiry process.
Evidence for the highest levels of achievement should be found in more than one section of the enquiry process. It does not have to be evidenced in every step.
When considering different sources of variation using primary data, ākonga should plan their data collection process carefully. As part of their explanation, they should give details about the different sources of variation that they anticipated or encountered, and the processes they put in place to manage these. When using secondary data, ākonga should consider what different sources of variation may have been present in the original data collection process and how these may have been managed. As part of their explanation, they may choose to explain how they would have managed sources of variation. Kaiako should ensure that all secondary data used allows ākonga to meet the requirements of the standard. Ākonga will need to explain at least two different types of sources of variation chosen from the list below.
Sources of variation include:
- Natural or real variation
- Occasion-to-occasion variation
- Measurement variation
- Induced variation
- Sampling.
Information about sources of variation can be found in this link: Sources of variation | NZ Maths
Appropriate visualisations include:
- scatter graph
- time series graph
- box and whisker plot
- two-way table
- bar or frequency graph of outcomes from a probability experiment
- long-run relative frequency graph.
Features must be described and justified for higher levels of achievement, using one or more visualisations. When doing so, ākonga may use a single visualisation with two or more features, or two or more visualisations, and give one or more features for each.
Collecting evidence
It is likely that most ākonga will use the statistical enquiry cycle — Problem, Plan, Data, Analysis, and Conclusion (PPDAC).
Participation in a brainstorm will allow ākonga greater understanding of their investigation but is not required for any level of achievement. Resulting ideas could be included or reflected across sections of the statistical enquiry process for higher levels of achievement.
Kaiako are able to use professional judgement when considering ākonga participation in the data collection process — detail of discussions around plans does not need to be recorded. A tick list of participation is sufficient.
Sourcing data may involve physical collection (taking measurements as an example), creating a questionnaire, collecting data from the internet, or other valid collection methods.
Sourced data should be appropriate to ākonga and their environment.
Possible contexts
At all times during the statistical enquiry process, data should be handled as taonga. Sensitivity regarding the types of data sourced about ākonga, whānau, or people groups is critical to providing a safe learning environment. Data that has the potential to lead to negative implications or perceptions for any person or people group should be avoided. Care should be taken when choosing investigative questions.
CensusAtSchool TataurangaKiTeKura is a useful resource for exploring real data that is relevant to ākonga in Aotearoa New Zealand.
The intent of the standard
The purpose of this Achievement Standard is to enable ākonga to show their capabilities when exploring data, following an established statistical enquiry process.
Ākonga will use a statistical enquiry process to source data and carry out an investigation. For Achievement, there is greater emphasis on how data is sourced or collected, presented, and analysed. For higher levels of achievement, ākonga will provide evidence across the chosen enquiry process.
It is intended that ākonga will have the opportunity to explore the context before beginning their independent work. This could include brainstorming in groups or with the whole class, with kaiako support, to gain a greater understanding of potential purposes behind an investigation.
The intent of the Achievement Standard is to complete an investigation using a statistical enquiry process. Some end points are complex or difficult to define. Ākonga should present evidence for a completed enquiry process for higher levels of achievement.
The following sections show further details for each of the four different styles of investigation.
Relationship investigation
The intent of a relationship investigation is to collect or source data and describe any visible trend including direction and strength, as well as groups and unusual values. Ākonga should relate the features that they describe closely to the context. It is not appropriate to refer to x and y.
Relationship investigations are useful for making predictions. A completed investigation needs to include a prediction. All predictions made should be informal. Predictions could be made using substitution into a trend line formula or by visual inspection of the graph. Regression analysis lies outside the scope of this Achievement Standard.
Features of the data may include:
- direction and strength of relationship
- clusters
- unusual or interesting data points
- patterns.
Comparison investigation
The intent of a comparison investigation is to collect or source data, describe features comparatively, and make an informal sample to population inference. When using a sample with between 20 and 40 in each group, ākonga will use the three-quarters/half rule to make a call where it is clear, and visually use the distance between medians as proportion of “overall visible spread” where a call is not clear. When using a sample with 100 or 1000 in each group, they will visually use the distance between medians as proportion of “overall visible spread” to make a call. The following is a link that provides support related to making a call:
Guidelines for “How to make the call” (censusatschool.org.nz).
For samples with uneven group sizes, the size of the smaller group will determine the method for making a call. Students are expected to demonstrate the difference between a sample and a population.
Dot plots, stem and leaf graphs, or histograms on their own do not provide sufficient evidence for discussing features. They can be used as supporting evidence in conjunction with a box and whisker graph.
When sourcing data from digital or readily available data sets, samples of size 100 or 1000 per category are recommended.
Features of the data may include:
- centre
- spread
- shape
- shift and overlap of two groups
- clusters
- unusual or interesting data points.
Time series investigation
The intent of a time series investigation is to collect or source data and describe any trends, seasonality/cycles, patterns, variation, and unusual values. Time series investigations are useful for making future forecasts. A completed investigation needs to include a forecast. All forecasts should be informal. Forecasts could be made using a visual inspection of the graph. Formal long-term trend line analysis lies outside the scope of this Achievement Standard. As part of their investigation ākonga may reason that a forecast is not useful. For higher levels of achievement this should be with justification, with non-trivial explanations and extended abstract thinking at the highest levels of achievement.
Features of the data may include:
- trend of time series
- unusual or interesting data points, spikes, or troughs
- seasonality, cycles
- patterns.
Experimental probability investigation
The intent of an experimental probability investigation is to conduct an experiment to collect data and describe observed probabilities in context. In some situations, with theoretical probabilities it may be appropriate to use simple simulations. Simulations could also be run with collected data where a theoretical model does not exist. An experiment using a tool with a simple outcome (dice, spinner) needs to use digital simulation to be at the right level.
Features of the data may include:
- clusters
- unusual or interesting data points
- centre
- spread
- shape
- patterns.
Making reliable judgements
To explore data effectively requires sufficient data — each style of investigation has different minimum recommendations:
- Relationship — 30 pairs of data.
- Comparison — 30 pieces of data from each category explored.
- Time series — 5 complete cycles.
- Experimental probability — 30 trials.
Using a statistical enquiry process usually requires ākonga to work through a set of steps. Evidence submitted should be marked holistically against a whole statistical enquiry process.
Evidence for the highest levels of achievement should be found in more than one section of the enquiry process. It does not have to be evidenced in every step.
When considering different sources of variation using primary data, ākonga should plan their data collection process carefully. As part of their explanation, they should give details about the different sources of variation that they anticipated or encountered, and the processes they put in place to manage these. When using secondary data, ākonga should consider what different sources of variation may have been present in the original data collection process and how these may have been managed. As part of their explanation, they may choose to explain how they would have managed sources of variation. Kaiako should ensure that all secondary data used allows ākonga to meet the requirements of the standard. Ākonga will need to explain at least two different types of sources of variation chosen from the list below.
Sources of variation include:
- Natural or real variation
- Occasion-to-occasion variation
- Measurement variation
- Induced variation
- Sampling.
Information about sources of variation can be found in this link: Sources of variation | NZ Maths
Appropriate visualisations include:
- scatter graph
- time series graph
- box and whisker plot
- two-way table
- bar or frequency graph of outcomes from a probability experiment
- long-run relative frequency graph.
Features must be described and justified for higher levels of achievement, using one or more visualisations. When doing so, ākonga may use a single visualisation with two or more features, or two or more visualisations, and give one or more features for each.
Collecting evidence
It is likely that most ākonga will use the statistical enquiry cycle — Problem, Plan, Data, Analysis, and Conclusion (PPDAC).
Participation in a brainstorm will allow ākonga greater understanding of their investigation but is not required for any level of achievement. Resulting ideas could be included or reflected across sections of the statistical enquiry process for higher levels of achievement.
Kaiako are able to use professional judgement when considering ākonga participation in the data collection process — detail of discussions around plans does not need to be recorded. A tick list of participation is sufficient.
Sourcing data may involve physical collection (taking measurements as an example), creating a questionnaire, collecting data from the internet, or other valid collection methods.
Sourced data should be appropriate to ākonga and their environment.
Possible contexts
At all times during the statistical enquiry process, data should be handled as taonga. Sensitivity regarding the types of data sourced about ākonga, whānau, or people groups is critical to providing a safe learning environment. Data that has the potential to lead to negative implications or perceptions for any person or people group should be avoided. Care should be taken when choosing investigative questions.
CensusAtSchool TataurangaKiTeKura is a useful resource for exploring real data that is relevant to ākonga in Aotearoa New Zealand.
Standard Exclusions
This Standard has exclusion(s). Standards that recognise the same or similar learning outcomes as other Achievement or Unit Standards need to be excluded to prevent ‘double dipping’. Where two or more Standards assess the same learning outcome, those Standards are specified in the Exclusions List. You can only use credits gained from one of these Standards towards your NCEA qualification.
Click here for the exclusions list for the new NCEA Level 1 pilot Standards.
Standard Exclusions
This Standard has exclusion(s). Standards that recognise the same or similar learning outcomes as other Achievement or Unit Standards need to be excluded to prevent ‘double dipping’. Where two or more Standards assess the same learning outcome, those Standards are specified in the Exclusions List. You can only use credits gained from one of these Standards towards your NCEA qualification.
Click here for the exclusions list for the new NCEA Level 1 pilot Standards.
Literacy and Numeracy Requirements
This Achievement Standard has been approved for numeracy in the transition period (2024-2027).
Full information on the co-requisite during the transition period: Standards approved for NCEA Co-requisite during the transition period (2024-2027).
Literacy and Numeracy Requirements
This Achievement Standard has been approved for numeracy in the transition period (2024-2027).
Full information on the co-requisite during the transition period: Standards approved for NCEA Co-requisite during the transition period (2024-2027).
Examples of Expected Student Responses
Examples of Expected Student Responses
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- Title: MS 1.1 Expected Student Response
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- MS 1.1 Expected Student Response.pdf
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- Title: MS 1.1 Expected Student Response
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