# Assessment Report

Level 3 Statistics 2019

### Part A: Commentary

Candidates who experienced success in these standards were able to complete accurate calculations and show understanding of concepts by making contextual statistical comments.  They displayed strong statistical literacy, using and applying statistical language appropriately to write precise answers that contained all necessary information.  These candidates supported their statements with statistical and/or numerical evidence in sufficient detail so that their chain of thinking is evident.

Weaker candidates knew very little about statistical terms and used little statistical terminology, often writing illegibly or profusely without answering the question being asked.  Candidates are advised to read the questions carefully, and then consider what was being asked of them by highlighting or underlining key words that allows them to better focus their responses. In some cases, candidates provided what might have been a great answer except that it was unrelated to the specific question that was asked.

Candidates are reminded that their writing must be legible and that rounding of calculations should be left until the final step of working.

## 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
• calculated a margin of error (MOE) and could articulate why a MOE is calculated
• 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
• recognised random allocation as a key idea in experimental design.

Candidates whose work was assessed as Not Achieved commonly:

• could not identify control and treatment groups in an experiment
• were unable to identify an explanatory and response variable
• did not refer to the statistical nature of the reports
• were unable to calculate the margin of error
• did not describe why the MOE is used
• 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.

Candidates who were awarded Achievement with Merit commonly:

• 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
• 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 30-70% range mean that the rule of thumb margin of error overestimates the actual MOE
• explained that when collecting data for a survey 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.

Candidates were required to assess the quality of reports using statistical methods indicated by the question, whether it was to do with the design of the study, or to identify potential issues with aspects reported in the study.

Candidates need to avoid generic, learned answers, for example “old people do not have the internet”, or “vehicle kilometres were measured twice for researchers to gain accurate data” without considering the context of the report or providing necessary explanation to relate their observations back to the statistical reports.

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 by describing the confidence interval in context and appropriately discuss the underlying population. For example, if the confidence interval was [6.2%, 19.4%], then candidates needed to interpret this correctly by saying something like “ I am pretty sure that the percentage of Marlborough shoppers who occasionally use plastic bags is between 6.2% and 19.4% higher than those who regularly do” before answering the claim.

Candidates need to be able to identify, describe and discuss both Experimental and Observational studies and apply that knowledge. Further, it is a good idea to mention what type of study the report is even if it is not clear from the question that it needs to be identified.

## 91585:  Apply probability concepts in solving problems

Candidates who were awarded Achievement commonly:

• calculated and compared two conditional probabilities to make a decision
• constructed and used a probability tree to make a decision
• processed statistical information to find a proportion.

Candidates whose work was assessed as Not Achieved commonly:

• gave frequencies as answers for probabilities, or accepted probabilities greater than one
• did not label calculated probabilities when there were more than one in a question
• made incorrect decisions when deciding between the use of conditional probabilities and other probabilities
• appeared to have stock answers which they tried to apply - these usually related to sample size, margin of error, independence.

Candidates who were awarded Achievement with Merit commonly:

• calculated and compared risks correctly
• justified independence as required
• selected an appropriate method to solve a problem
• thought beyond the question and gave examples to support their statements
• considered systemic issues when asked to apply probabilities in predicting an outcome/apply probabilities to a different cross section of people.

Candidates who were awarded Achievement with Excellence commonly:

• interpreted and reasoned by giving a statement and clearly explaining the impact
• evaluated the validity of an assumption
• identified what the question was referring to and were able to ensure they covered that in their answer
• discussed why it may not be appropriate to apply a probability model in a particular context.

Candidates had the opportunity to make use of two-way tables, probability trees and Venn Diagrams.  Candidates were tested on their understanding of simple probability, conditional probability and independence in real life contexts.

Candidates would benefit from knowing more than one way of establishing independence, and by knowing the difference between ‘times as likely’ and ‘times more likely’.  Many candidates had little idea about the concept of using a simulation to support a decision.

Candidates were able to give good comments, which showed understanding of concepts but were not completing calculations correctly.

## 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 terms such as ‘at least’ and ‘no more than’
• calculated the mean from a graph
• calculated a probability using data from a graph
• identified the correct parameters needed to solve a probability distribution problem
• could accurately draw a normal distribution graph
• could identify the conditions required for probability distributions.

Candidates whose work was assessed as Not Achieved commonly:

• applied an inappropriate distribution model to a problem
• could not draw a graph of a normal distribution
• could not calculate a given probability for a normal, poisson, binomial or triangular distribution
• misinterpreted inequalities written as text
• could not calculate the mean from a graph
• could not calculate a probability from a bar graph
• gave a probability answer greater than one
• made calculation errors or rounded too severely.

Candidates who were awarded Achievement with Merit commonly:

• completed multi-step problems across a range of distributions
• identified assumptions involved in using probability distribution models and related these to the context of a problem
• explained the limitations of the chosen probability distribution model in terms of context
• could describe features of distributions (shape, symmetry, spread, centre) and compare these to the distributions of the data they had been given
• understood concepts such as independence, constant rate or constant probability, and randomness, and could explain these in terms of the context of a 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:

• showed a depth of understanding across a range of distributions, appropriately linking statistical and contextual information
• 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 multi-step probability distribution problems
• could calculate a percentage reduction
• clearly explained their reasoning and justified decisions
• used statistical reasoning to evaluate a claim
• evaluated a model by comparing experimental data with the features of a distribution.

The paper highlighted candidate confusion and misconceptions around a number of terms and concepts: in particular independence. Many confused independence of an event with the probability of the event.  Some were unclear on the relationship/ difference between a mean, median and mode.  Some candidates were also unclear about the difference between the conditions of a probability distribution model and an assumption made when applying the model.

Candidates need to be able to explain how the conditions and/or features of a probability distribution model (e.g. randomness, independence, symmetric, bell-shaped, unimodal) are appropriate or inappropriate to the given context.  To gain Merit or Excellence candidates need to demonstrate proficiency in a number of distributions.

When given a graph of real data, candidates need to consider the information presented in the graph before applying a probability distribution model. Many candidates assumed the distribution without considering using the raw data in calculations first.

Candidates need to be able to identify features of a graph and to compare these to the features of probability distribution models. It is expected that numerical and probability evidence will be provided in support of arguments as to why a particular model is appropriate to use for this data.

### Mathematics and Statistics subject page

Previous years' reports

2018 (PDF, 139KB)

2017 (PDF, 52KB)

2016 (PDF, 228KB)