Statistics
Level 1
Statistical investigation
AO1: Conduct investigations using the statistical enquiry cycle:
This means students will collect, sort and count data. Students will mostly encounter category data.
This data arises from classifying, for example sorting data into colour categories.
Simple number data generated through measurement with whole units is also manageable.
Students should become familiar with displaying category data using pictographs, set diagrams and bar charts.
Discussion should centre on similarities and differences between categories,
for example “Six more people like hokey-pokey ice cream than vanilla”.
Click to download a PDF of second-tier material relating to Level 1 Statistical Investigations (632KB)
Statistical literacy
AO1: Interpret statements made by others from statistical investigations and probability activities. This means students will match comments made by others, usually their classmates, with the features of displays. These displays will be showing category data as pictographs, set diagrams, and bar charts.
Probability
AO1: Investigate situations that involve elements of chance, acknowledging and anticipating possible outcomes. This means students will consider the possible outcomes of events. Possible outcomes can be listed, for example when tossing a coin the outcomes are heads and tails. The possible outcomes should be the basis for predictions rather than perceptions of luck.
Click to download a PDF of second-tier material relating to Level 1 Probability (125KB)
Level 2
Statistical investigation
AO1: Conduct investigations using the statistical enquiry cycle:
This means students will use the statistical enquiry cycle in their investigations.
The cycle has five phases that relate to each other. Some enquiries follow these phases
in sequence but often new considerations mean that a statistician must go back to previous phases and rethink. The phases are:
At Level Two students should be able to pose questions that they want to investigate,
consider the appropriate data they need to collect, gather and sort the data in
order to develop an answer to their question. The data involved may be either
category data or whole number data. Category data arises from classifying and the
interest is in how many of the data items fall in each category (called frequency).
Colour and number of doors are two ways to classify cars that will produce category data.
Whole number data comes from situations where only whole number values are possible, e.g.
how many people live in your house? or from rounding of measures, e.g. how long is your pencil
to the nearest centimetre? The most common graphs for displaying category data are pictographs,
bar, strip and pie graphs. Whole number data can be displayed using dot plots or stem and leaf
graphs. Students should communicate their result through reference to their data displays with an
emphasis on similarity and difference, e.g. boys like outdoor games more than girls..
Click to download a PDF of second-tier material relating to Level 2 Statistical Investigations (584KB)
Statistical literacy
AO1: Compare statements with the features of simple data displays from statistical investigations or probability activities undertaken by others. This means students will critically consider comments made by others, usually their classmates, by referring to the features of displays on which the person is making claims. These displays will be showing either category data (pictographs, bar, strip, and pie graphs) or whole number data (dot plots or stem and leaf graphs). Students should also consider whether the chosen display/s best shows patterns in the data, e.g. strip and pie graphs show proportions well, pictographs and bar graphs show differences well.
Probability
AO1: Investigate simple situations that involve elements of chance, recognising equal and different likelihoods and acknowledging uncertainty. This means students will recognise that probability is about the chance of outcomes occurring. Through activities that involve them personally, students at Level Two are expected to consider the possible outcomes of events in predicting what might occur. Through carrying out experiments, e.g. playing a game of chance, and making simple models of all the outcomes, e.g. lists or tables, students should recognise when outcomes appear to be equally likely, e.g. getting an even number when tossing a dice. Students should also recognise that where an event has more than one possible outcome they cannot predict the outcome with certainty, e.g. "it probably won’t be a six but it might be" when rolling a dice. Students should relate probability to events in their daily life, e.g. "it is very likely to rain today".
Click to download a PDF of second-tier material relating to Level 2 Probability (74KB)
Level 3
Statistical investigation
AO1: Conduct investigations using the statistical enquiry cycle:
The statistical enquiry cycle has five phases that relate to each other. Some enquiries follow these phases in sequence but
often new considerations mean that a statistician must go back to previous phases and rethink. The phases are:
At Level Three students should be able to pose questions that they want to investigate, consider the appropriate data they need to collect, gather and sort the data in order to develop an answer to their question. The data involved should be multivariate so it should include many variables, e.g. gender, age, height, eye colour, bedtime, etc., so that relationships between the variables can be explored. Students should be able to ask summary questions (of a variable), e.g. what is the usual range in heights for 10 year old students?, comparison questions, e.g. are girls taller than boys?, and relationship questions, e.g. do older students go to bed later than younger students. Data displays, including tables and graphs, expected at Level Three are tally charts, frequency tables, pictographs, bar graphs, strip graphs, and pie charts for category data, dot plots and stem and leaf graphs for whole-number data, and simple line graphs for time series data. Students should be able to use computer technology to create these displays to find patterns, including trends over time, in data as well as to communicate their findings to others. They should be able to justify their choice of display/s with reference to the patterns they wish to highlight.
Click to download a PDF of second-tier material relating to Level 3 Statistical Investigations (171KB)
Statistical literacy
AO1: Evaluate the effectiveness of different displays in representing the fi ndings of a statistical investigation or probability activity undertaken by others. This means students will learn to become critical consumers of statistically based information. This involves critically analysing the choice of display other people have made to convey statistical information. At Level Three students should be able to gain information from all of the displays mentioned in Statistical Investigation, and be aware of the type of data each display is appropriate for and the kind of pattern or relationship that the display is best at communicating. For example, pictographs, and bar graphs highlight difference between frequencies of categories, e.g. four more students have blue eyes than green, while pie charts and strip graphs highlight proportions, e.g. the spinner landed on red about one third of the time. Students should link the claims made by others with the appropriateness of the displays used.
Probability
AO1: Investigate simple situations that involve elements of chance by comparing experimental results with expectations from models of all the outcomes, acknowledging that samples vary. This means students will understand that probability is about the chance of outcomes occurring. At Level Three students should recognise that it is not possible to know the exact probability of something occurring in most everyday situations, e.g. The chance is of a day in March being fine. They should understand that trialling must be used to gain information about the situation and that the results of trial samples vary, e.g. March 2008 is likely to be different from March 2009. Contrived chance events are used to highlight the variation between expected outcomes from models, and experimental outcomes from trialling. Level Three students are expected to use systematic methods such as listing, tree diagrams, or tables to find all the possible outcomes of simple situations such as tossing coins, drawing cards, or rolling dice. They should accept that experimental samples from those situations, e.g. tossing a coin ten times, vary from one another, and from the proportions expected from a model, i.e. most times five heads do not come up.
Click to download a PDF of second-tier material relating to Level 3 Probability (116KB)
Level 4
Statistical investigation
AO1: Plan and conduct investigations using the statistical enquiry cycle:
This means students will use the statistical enquiry cycle to plan and conduct investigations. The cycle has five phases that relate to each other.
Some enquiries follow these phases in sequence but often new considerations mean that a statistician must go back to previous phases and rethink. The phases are:
At Level Four students should be able to pose questions that they want to investigate, consider the appropriate data they need to collect, gather and sort the data in order to develop an answer to their question. The data involved should be multivariate s (include many variables, e.g. gender, age, height, eye colour, bedtime, etc.) so that relationships between the variables can be explored. Students should be able to ask summary questions (of a variable), e.g. what is the usual range in heights for 10 year old students?, comparison questions, e.g. Are girls taller than boys?, and relationship questions, e.g. do older students go to bed later than younger students? They should be able to decide which variables are important for answering their question, e.g. quality of a sports player might be determined by points scored, assists, defensive turnovers or other variables. Students should also consider their methods of data collection, considering issues such as manageability, sampling, surveying, data safety, and technology use. Data displays, including tables and graphs, expected at Level Four are tally charts, frequency tables, pictographs, bar graphs, strip graphs, and pie charts for category data, dot plots, stem and leaf graphs and scatterplots for measurement data, and line graphs for time series data. Students should be able to use computer technology to create these displays to find patterns in the data, including differences and similarities between distributions, e.g. boys’ heights compared to girls, clusters and outliers within distributions, e.g. middle and spread, associations of variables, e.g. height with armspan, trends over time, e.g. cellphone use over a day, as well as to communicate their findings to others. They should be able to justify their choice of display/s with reference to the patterns they wish to highlight.
Click to download a PDF of second-tier material relating to Level 4 Statistical Investigations (185KB)
Statistical literacy
AO1: Evaluate statements made by others about the findings of statistical investigations and probability activities. This means students will critically evaluate the strength of arguments proposed by others that is supported by statistical information. At Level Four students should consider features of the statistical investigation of others in weighing the strength of the findings. These features include the appropriateness of sampling methods (e.g. number, representativeness), quality of the data collection (e.g. questions asked, accuracy of measurement, fairness of the experiment), data analysis (technology use, choice of displays) and the extent to which claims made are supported by the evidence.
Probability
AO1: Investigate situations that involve elements of chance by comparing experimental distributions with expectations from models of the possible outcomes, acknowledging variation and independence. This means students will understand that probability is about the chance of outcomes occurring. At Level Four students should recognise that it is not possible to know the exact probability of something occurring in most everyday situations, e.g. the probability of someone being left-handed. They should understand that trialling must be used to gain information about the situation and that the results of trial samples vary, e.g. different samples of 100 people will have different proportions. Contrived chance events are used to highlight the variation between expected outcomes from models, and experimental outcomes from trialling. Level Four students are expected to use systematic methods such as listing, tree or network diagrams, and tables to find all the possible outcomes of simple one or two stage situations such as tossing two coins, drawing counters from a bag, or rolling two dice. Students should compare the distributions they get from trialling with the expectations obtained from models, accepting variation between samples and that the results of one sample do not impact on the next (independence), e.g. Take samples of twenty counters, with replacement, from a bag that has one-half red, one-third blue and one-sixth yellow. Accept that an eight red, seven blue, and five yellow result is natural and that it will not be compensated by the next sample.
AO2: Use simple fractions and percentages to describe probabilities. Simple fractions and percentages in this objective are common benchmarks like one half (50%), thirds (33.3% and 66.6%), quarters (25% and 75%), fifths (20%, 40%, 60%, 80%), tenths (10%, 30%, etc). Students should know that outcomes that are certain are described by fractions equalling one, including 100%, and outcomes that are impossible are described by fractions equalling zero, including 0%. In contrived situations involving elements of chance, e.g. totalling two dice, students should know that the count of all possible outcomes gives the denominator of a probability fraction, e.g. 36 possible outcomes, and the number of desired outcomes gives the numerator, e.g. there are 9 ways to get a total of either 2,4 or 6 so the probability is 9/36 or 1/4 . In realistic situations where probabilities are estimated, e.g. the chance of a drawing pin landing safe, students are expected to accept variation from an exact fraction, e.g. 37 out of 100 were safe which is about or 33.3%..
Click to download a PDF of second-tier material relating to Level 4 Probability (154KB)
Level 5
Statistical investigation
AO1: Plan and conduct surveys and experiments using the statistical enquiry
cycle:
Further detail on this Achievement Objective will be added shortly.
Click to download a PDF of second-tier material relating to Level 5 Statistical Investigations (288KB)
Statistical literacy
AO1: Evaluate statistical investigations or probability activities undertaken by others, including data collection methods, choice of measures, and validity of findings. Further detail on this Achievement Objective will be added shortly.
Probability
AO1: Compare and describe the variation between theoretical and experimental distributions in situations that involve elements of chance. Further detail on this Achievement Objective will be added shortly.
AO2: Calculate probabilities, using fractions, percentages, and ratios. Further detail on this Achievement Objective will be added shortly.
Level 6
Statistical investigation
AO1: Plan and conduct investigations using the statistical enquiry cycle:
Further detail on this Achievement Objective will be added shortly.
Statistical literacy
AO1: Evaluate statistical reports in the media by relating the displays, statistics, processes, and probabilities used to the claims made. Further detail on this Achievement Objective will be added shortly.
Probability
AO1: Investigate situations that involve elements of chance:
Further detail on this Achievement Objective will be added shortly.
