The Curriculum Indicators
AO-S7-1 Uses the statistical enquiry cycle to conduct surveys and experiments and
to analyse existing data sets.
 Selects and uses appropriate sampling methods, for example, simple random,
systematic, stratified, cluster, and quota.
 Evaluates sampling method used, for example, is a sample sufficiently large,
randomly chosen, and representative of the population.
 Collects and manages data.
 Uses exploratory data analysis to explore features of the data:
o Uses appropriate statistical graphs and tables to explore the data and
communicates relevant detail and overall distributions.
o Uses appropriate measures to communicate features of the data.
 Uses relevant contextual knowledge when communicating findings.

statistical inferences.
o Communicates findings in a report which includes:
 relevant summary statistics, graphs and tables to support the findings of
the survey
 quantitative and qualitative statements
 statistical inferences
 justified conclusions.
AO 7-2 Make Inferences from Surveys
B Using sample statistics to make point estimates of population parameters.
Understands that the sample statistics can be used as point estimates of the
population parameters, for example, sample medians and IQRs can be used as
point estimates for population medians and IQRs, or sample proportions for
population proportions when using categorical data.
C. Recognising the effect of sample size on the variability of an estimate:
Within the context of an investigation of observed data:
o Finds informal confidence intervals for population medians.
o Plots sample data showing informal confidence intervals (median ± 1.5 IQR / √n)
on boxplots.
o Uses an informal confidence interval to make an inference about the population
median from sample data plot.
o Makes a claim about whether one group has larger values than another group
using informal confidence intervals for the population medians.
o Explains the connections among sample, population, sampling variability,
sample size effect, informal confidence interval, and degree of confidence.
See key mathematical ideas on NZmaths.
CensusAtSchool is a valuable website for classroom activities and information for
teachers on all things statistics. Kiwi Kapers (see context elaborations for S7-1)
CLARIFICATIONS
An important understanding is that the random samples are being used to talk
about the population groups. There needs to be clear links between the
investigative question, the analysis and the conclusion
Problem
 The purpose of the investigation needs to be clear.
 Students must demonstrate an understanding of the population from which the
sample will be taken.
 The investigative question that is posed must involve a comparison. The
investigative question needs to:
 identify the variables, for example gender and height
 identify the population groups, for example NZ year 12 girls and NZ year 12 boys
 include a statement about a population parameter which will give an indication
of what the student thinks the result will be, for example NZ year 12 boys are
taller than NZ year 12 girls
 identify the population parameter.
91264 Use statistical methods to make an inference
Achievement
Achievement with Merit
Achievement with Excellence
 Use statistical methods to
make an inference.
 Use statistical methods to
make an inference, with
justification.
 Use statistical methods to
make an inference, with
statistical insight.
Explanatory Notes
1
This achievement standard is derived from Level 7 of The New Zealand Curriculum,
Learning Media, Ministry of Education, 2007; and is related to the achievement objectives
 carry out investigations of phenomena, using the statistical enquiry cycle:
 using existing data sets
 evaluating the choice of sampling and data collection methods used
 using relevant contextual knowledge, exploratory data analysis, and statistical
inference
 make inferences from surveys:
 using sample statistics to make point estimates of population parameters
 recognising the effect of sample size on the variability of an estimate
in the Statistics strand of the Mathematics and Statistics Learning Area. It is also related to
the material in the Teaching and Learning Guide for Mathematics and Statistics, Ministry of
Education, 2010 at http://seniorsecondary.tki.org.nz.
2
3
Use statistical methods to make an inference involves showing evidence of using each
component of the statistical enquiry cycle to make an inference.
Use statistical methods to make an inference, with justification involves linking components
of the statistical enquiry cycle to the context, and/or to the populations, and referring to
evidence such as sample statistics, data values, trends, or features of visual displays in
support of statements made.
Use statistical methods to make an inference, with statistical insight involves integrating
statistical and contextual knowledge throughout the statistical enquiry cycle which may
involve reflecting on the process, or considering other explanations.
Using the statistical enquiry cycle to make an inference involves:
 posing an appropriate investigative comparison question from a given set of
population data
 selecting random samples
 selecting and using appropriate displays and measures
 discussing sample distributions
 discussing sampling variability, including the variability of estimates
 making an inference
 communicating findings in a conclusion.
Plan and Data
 The investigation involves selecting random samples from the population groups and using
information from the samples to make an inference about the population groups.
Analysis
 The informal confidence intervals for the population medians are required and need to be
used to answer the comparison investigative question. At Achieved level it is sufficient to show
the informal confidence intervals on the graph. At Merit level and above the informal
confidence intervals must be given in context. For example, ‘I am pretty sure that the median
height for NZ year 12 boys is somewhere between xxx and yyy'.
 In discussing the sample distributions, the discussion must be about the distributions of the
variables, for example the heights of NZ year 12 boys and NZ year girls.
 The discussion needs be in context at all levels. The context includes the variable, for example
height, numerical values and associated units and the population groups.
Conditions of Assessment
All Standards
Assessment tasks are designed so that each task provides opportunity for students to
provide evidence for all grades. There are not separate tasks for each grade. Holistic
decisions will be used in the awarding of a grade by reference to the achievement criteria
in the standard.
Internal assessment provides considerable flexibility in the collection of evidence. Care
must be taken to allow students opportunities to present their best evidence against the
standard that is free from unnecessary constraints. Collection of evidence for these
standards could include, but is not restricted to, an extended task, an investigation, or a
more formal activity.
Students are expected to have access to appropriate technology. For statistics standards
this would include statistical software.
Authenticity of student evidence needs to be assured. For example, for an investigation
carried out over several sessions, this could include teacher observations or the use of
milestones such as meetings with students, or journal entries of progress etc.
Achievement Standard
Number
91264 Mathematics and Statistics
2.9
Title
Use statistical methods to make an
inference
Number of Credits
4
Version
1
Assessment of this standard involves an investigation. Sufficient time should be
allowed for students to complete the investigation.
It is intended that students have access to a set of population data from which
they are to pose a comparative question and then take random samples to
analyse in order to answer that question. The population data set must be
sufficiently large enough to show a need to sample.
The context must be familiar to students and background detail provided with the
data set.
A further assessment opportunity must involve a new set of population data with a
new context.
Conclusion
 Students must make an inference, which will be a conclusion about the population
medians based on their samples taken from the population.
 The conclusion must be consistent with the analysis. It will answer the posed
investigative question and will involve making a call about the population medians.
 The informal confidence intervals will be used to make an inference about the
population medians. If there is no overlap in the informal confidence intervals an
appropriate inference is that the population median for ‘A’ is greater than the
population median for ‘B’. If there is an overlap in the informal confidence intervals
there is not enough evidence to make a call that the population median for ‘A’ is
greater than the population median for ‘B’.
 At Merit and above, an interpretation of the informal confidence intervals are
required.
 An understanding relating to sampling variability and variability of estimates must be
evident. Another sample will give different medians and informal confidence
intervals.