Achievement objective S71
In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:
 Carry out investigations of phenomena, using the statistical enquiry cycle:
 A. conducting surveys that require random sampling techniques, conducting experiments, and using existing data sets
 B. evaluating the choice of measures for variables and the sampling and data collection methods used
 C. using relevant contextual knowledge, exploratory data analysis, and statistical inference.
Indicators
 Uses the statistical enquiry cycle to conduct surveys and
experiments and to analyse existing data sets.
 Conducts surveys to find solutions to problems (or uses existing data sets):
 Poses survey questions, considering
sources of variation, for example, what are the variables to be collected, how each variable will be measured.
 Designs, trials, and improves
questionnaires using a range of appropriate questions types, checking the survey questions using, for example,
desk review, conducting
pilot surveys.
 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:
 Uses appropriate
statistical graphs and tables to explore the data and communicates relevant detail and overall distributions.
 Uses appropriate
measures to communicate features of the data.
 Uses
relevant contextual knowledge when communicating findings.
 Makes
statistical inferences.
 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.
 Conducts
experiments to find solutions to problems:
 Poses investigative questions about an experimental situation.
 Plans experiments:
 Considers
sources of variation, for example, what are the variables to be collected, how each variable will be measured.
 Evaluates the choice of variables and measures used in the experiment.
 Selects and uses appropriate data collection and recording methods.
 Conducts the experiment and collects data.
 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.
 See
key mathematical ideas on NZmaths.
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Progression
S71 links from S61 and to S72, S73, S81.
What is new/changed?
 Conducting experiments.
 Use of exploratory data analysis.
 Using relevant contextual knowledge (given).
Possible context elaborations

CensusAtSchool is a valuable website for classroom activities and information for teachers on all things statistics.
 You have been asked by the Ministry of Health to design a questionnaire that would enable them to find out more about the effects of high sugar intake on teenagers.
 Investigate a given claim from the media, where the raw data is available.

Conduct an experiment to see if drinking a caffeinated drink improves reflexes, or memory, or athletic performance.

Kiwi Kapers – uses a simulated data set of Kiwis to explore some of the big ideas.
 Sampling variation and making inferences:
 Teaching notes
 Data cards
 Information about the variables
 Population graphs and statistics
 Blank dot plot sheet for collecting weights
 Kiwi data in Excel
 Kiwi data in Fathom
 Deciding on the sample size:
 Teaching notes
 Student worksheet
 Fathom taking samples
 Example of output (different sample sizes)
 Fathom collecting sample medians
 Example of output (sample medians)
 Example of output (collation of class medians)

Introduction to stratified sampling:
 Teacher notes
 Dot plot blank sheet for collecting heights
 Data cards
 Kiwi population (excel)
 Fathom taking samples
 Example of output (samples)
 Fathom taking counts of species

PPDAC cycle – using stratified sampling:
 Teacher notes
 Student worksheet
 School population (fathom)
 School population (excel)
 Fathom file for taking sample
 Fathom file used for teacher notes
 Two further examples that can be used for the entire statistical enquiry cycle. Set up for sampling:
 the kiwi population is the same as used in Kiwi Kapers and introduction to stratified sampling:
 Fathom file for taking sample
 Kiwi population (excel)
 Information about variables
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Assessment for qualifications
NCEA achievement standards at level 1, 2 and 3 have been aligned to the New Zealand Curriculum. Please ensure that you are using the correct version of the standards by going to the
NZQA website.
The following achievement standard(s) could assess learning outcomes from this AO:
 AS91263 Mathematics and statistics 2.8 Design a questionnaire
 AS91264 Mathematics and statistics 2.9 Use statistical methods to make an inference
 AS91265 Mathematics and statistics 2.10 Conduct an experiment to investigate a situation using statistical methods
Refer to the
mathematics and statistics matrix.
Last updated March 26, 2018
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