 Home
 Studying in New Zealand
 Qualifications and standards
 NCEA
 Māori & Pasifika

Providers and partners
 About education organisations
 NZQA's quality assurance system for tertiary education organisations
 Quick links to NZQF documents
 Approval, accreditation and registration
 Consistency of graduate outcomes
 Monitoring and Assessment
 Selfassessment
 External evaluation and review
 Assessment and moderation of standards
 Submitting results and awarding qualifications
 The Education (Pastoral Care of International Students) Code of Practice
 Offshore use of qualifications and programmes
 Guidelines and forms
 About us
Assessment Report
Level 3 Statistics 2018
Standards 91584 91585 91586
Part A: Commentary
Candidates who performed well across the standards were able to display their knowledge of statistical and probability concepts, make accurate calculations and support their answers with statistical reasoning written in context. They showed a good level of statistical literacy, taking care to answer the particular question being asked.
Successful candidates demonstrated strong skills in working with probability theory and probability distributions as well as sound reasoning with data and models. They understood that true probability is unknown and that it can be estimated by a theoretical probability and/or the result from an experiment. These stronger candidates were able to analyse a statistical report, describing study designs, identifying confounding and linking these observations to the strength of a claim in context.
Weaker candidates often did not understand how to provide a statistical response, either failing to provide numerical evidence to support their responses, or providing numerical evidence without linking this evidence to the underlying context.
Part B: Report on standards
91584: Evaluate statistically based reports
Candidates who were awarded Achievement commonly:
 correctly identified control and treatment groups in an experiment
 identified an explanatory and response variable
 quoted directly from the report using important values
 calculated a margin of error
 knew that the rule of thumb for the MOE is invalid for a proportion outside of the 30%70% range
 calculated a confidence interval (without explanation)
 identified the difference between observational and experimental studies
 used the basic terminology for this standard (although may have inconsistently applied it)
 recognised random allocation as a key idea in experimental design but often did not explain why it was used or understand that random allocation helps to reduce bias, not eliminate it.
Candidates whose work was assessed as Not Achieved commonly:
 could not identify control and treatment groups in an experiment
 could not identify an explanatory and response variable
 quoted numerical values but not in context
 did not refer to the statistical nature of the reports
 did not use rule of thumb formula to calculate the margin of error
 failed to use the appropriate margin of error to calculate the relevant confidence interval for a comparison confidence interval
 could not identify a proportion outside of the 30%70% range
 knew very little about statistical terms and used little statistical terminology
 could not identify random allocation as a key idea in experimental design
 identified a key feature of a study design but failed to describe its relevance to the context
 wrote profusely without answering the question being asked
 did not use a “scatterplot” to show a correlation.
Candidates who were awarded Achievement with Merit commonly:
 explained how random allocation in an experiment reduces bias or creates two fair groups
 identified an issue with a survey and related it to representativeness with a specific population
 identified and described one issue with study design as opposed to survey design
 explained that percentages outside the 3070% range mean that the rule of thumb Margin of error overestimates the actual MOE
 explained that when collecting data for a survey that a representative sample is important
 identified and described a confounding variable with specific relation to one of the original variables
 analysed a statistical report, identifying observational versus experimental studies, distinguishing between correlation and causation (but not necessarily in great depth)
 calculated a comparison confidence interval but could not correctly interpret it within the context or justify why a claim was true
 commented on key features by referring to statistical evidence provided in the reports without specific details
 identified a population in context.
Candidates who were awarded Achievement with Excellence commonly:
 described an issue with study design and directly linked it to the strength of a claim in context
 calculated a comparison confidence interval and interpreted it in context, justifying a statistical claim using correct statistical language, including identifying the population
 identified and described a confounding variable, fully describing the interaction between both variables
 analysed a statistical report, identifying observational versus experimental studies, distinguishing between correlation and causation, and discussing specific language used in the report
 related their findings back to the report
 used and correctly applied statistical language
 wrote precise answers that contained all necessary information.
Standard specific comments
It is important for candidates to understand the effect of sample size on the margin of error. After calculating comparison confidence intervals candidates need to comment on the claim and appropriately discuss the underlying population.
Candidates need to avoid generic, learned answers, for example “old people do not have the internet” without considering the context of the report or providing necessary explanation to relate their observations back to the statistical reports.
Students would benefit from spending more time on statistical inference for experiments, so that they are able to explain that testing for differences between two group means is necessary before making a claim. Students also need to become familiar with examples of confounding variables and practicing recognising a range of nonsampling errors.
91585: Apply probability concepts in solving problems
Candidates who were awarded Achievement commonly:
 calculated relative frequencies
 understood the context of the question but failed to provide evidence which was sufficient to answer the question at a higher level
 could model a situation with a tree diagram
 could process information provided in a twoway table.
Candidates whose work was assessed as Not Achieved commonly:
 only gave numbers as answers rather than words to support them, and vice versa
 focused on sampling variability or sample size
 were unable to complete a twoway table or Venn Diagram
 gave probabilities greater than one
 believed that true probability was equal to the theoretical or experimental estimate did not understand the concept of mutually and independent events
 struggled with the concept of conditional probability
 only knew the one test for independence P(A∩B)=P(A)×P(B), not P(A│B)=P(A).
Candidates who were awarded Achievement with Merit commonly:
 understood conditional probability but couldn’t always explain their reasoning
 made errors in working but continued consistently to an answer
 were able to carry out complex calculations but struggled to give reasons or justification
 demonstrated a full understanding of mutually exclusive and independent events
 correctly modelled the situation involving three events.
Candidates who were awarded Achievement with Excellence commonly:
 clearly articulated their thoughts and backed up their statements with relevant probabilities
 understood that the true probability was unknown and that it could be estimated by a theoretical probability and/or a result from an experiment
 had a good level of statistical literacy and actually answered the question being asked
 used appropriate rounding at all levels
 stated assumptions clearly when appropriate
 integrated contextual and statistical knowledge
 could recognise when sampling with, and without, replacement was appropriate
 could interpret simulation results in context.
Standard specific comments
Candidates would benefit from improving their use of statistical terminology. In some cases the candidates were held back from obtaining higher grades by their lack of ability to express contexts appropriately.
There was some confusion when working with likelihood ratio (relative risk). A number of candidates used the words “... times more likely …” rather than “… times as likely …”.
91586: Apply probability distributions in solving problems
Candidates who were awarded Achievement commonly:
 selected appropriate probability distribution models
 calculated simple probabilities using probability distribution models
 understood factors that should be kept constant, when modelling practical situations
 understood terms such as ‘at least’ and ‘no more than’
 calculated the expected value of a discrete random variable from a table of probabilities
 could calculate a proportion from a graph
 identified the correct parameters needed to solve a probability distribution problem
 sketched distribution models in comparison to another model
 did not justify their choice of distribution model adequately.
Candidates whose work was assessed as Not Achieved commonly:
 applied an inappropriate distribution model to a problem
 could not draw a normal distribution graph
 could not calculate a given probability for a normal, Poisson or binomial distribution
 misinterpreted inequalities written as text
 could not calculate the expected value from a table
 could not use the correct mode of their graphics calculator or read probability tables correctly
 gave a probability answer greater than one
 could not label a triangular distribution with correct parameters
 made calculation errors or rounded too severely.
Candidates who were awarded Achievement with Merit commonly:
 completed multistep problems across a range of distributions; linking their responses to the stated context
 explained the limitations of the chosen probability distribution model in terms of context
 correctly calculated expected value, standard deviation, variance and probability and used these to solve problems
 used probability skills e.g. trees, independence, combined and conditional events in conjunction with distributions to solve problems
 understood the concept and purpose of standard deviation and variance in context
 could find inverse probabilities using the normal distribution
 recognised the use of continuity corrections in approximating discrete data with continuous distributions and applied this correctly
 understood the meaning of “either or” and “both” in a probability problem
 communicated their thinking using appropriate statements, e.g. stating probability distribution model and parameters, correctly using probability notation and providing evidence or calculations for any general statements they made.
Candidates who were awarded Achievement with Excellence commonly:
 discussed the appropriateness (or inappropriateness) of a probability distribution model by considering features of the probability distribution, statistical evidence and/or the context of the situation
 devised a strategy to solve multistep probability distribution problems
 clearly explained their reasoning and justified decisions
 used probability skills e.g. trees, independence, combined and conditional events in conjunction with distributions to solve multistep problems
 could complete expectation algebra calculations (particularly variance).
Standard specific comments
Candidates struggled to draw normal distribution graphs in relation to another normal graph.
The paper highlighted candidate confusion and misconceptions around a number of terms and concepts: in particular, independence, random and continuous. Some candidates used the term continuous when they meant boundedness and were unclear on the idea of randomness as it related to unpredictability. Some confused independence due to probability and the property for independence to do with variance.
Some candidates were also unclear on the relationship between variance and standard deviation.
Some candidates confused the Poisson distribution condition around rate and proportionality with the binomial condition that the probability remains constant. They were also unclear as to what a rate was in a particular context and when discussing it frequently confused the term proportional with probability.
Candidates need to be able to explain how the conditions and/or features of a probability distribution model (e.g. randomness, independence, symmetric, upper/lower bounds) are appropriate or inappropriate to the given context. They also need to be able to support their statements with statistical and/or numerical evidence in sufficient detail that their chain of thinking is evident.
Candidates would benefit from more time spent on continuity corrections as they were unsure how to apply them in context.
Candidates should leave rounding their working until the final step of working.
When given a graph of real data candidates need to consider the information presented in the graph before applying a probability distribution model. Candidates assumed a model of a discrete random variable without considering using the raw data in calculations first.
To gain Merit or Excellence candidates need to demonstrate proficiency in a number of distributions.
Mathematics and Statistics subject page
Previous years' reports
2016 (PDF, 228KB)