Interpreting statistical and chance situations

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Level Five
Statistics
Units of Work
This unit is intended to develop the critical thinking required to evaluate statistical reports prepared by others. To carry out this evaluation, students will need to be familiar with making valid statistical statements of provided data and the process of selecting and presenting statistical...
  • Comment on the validity of a statistical report with reference to:
    • sample size
    • proportions stated
    • central tendency
    • the presentation of data
    • data collection
  • Comment on the voice of a statistical report.

S5-4: Calculate probabilities, using fractions, percentages, and ratios.

This means that students will calculate probabilities for probability situations that involve two or more events.  These events may be independent (for example rolling two dice, or tossing two coins) or dependent (for example drawing two cards from a deck of cards without replacement, or choosing to students from the class at random).  They will be able to model these situations using models such as tree diagrams, tables and systematic lists and assign theoretical probabilities as proportions using fractions, percentages and ratios, for example the odds of winning the game are 2:3.

S5-3: Compare and describe the variation between theoretical and experimental distributions in situations that involve elements of chance.

Students at Level Five understand that elements of chance have an effect on the certainty of results from surveys or experiments. Through examples from real life they should understand that statistics usually involves situations where the actual probabilities are not known, for example, probability of catching a disease. They should recognise situations where deterministic theoretical models are not possible, for example chance of a bus being early, and distinguish them from situations where probabilities can be reasoned from all the possibilities.

S5-2: Evaluate statistical investigations or probability activities undertaken by others, including data collection methods, choice of measures, and validity of findings.

This means that students will evaluate the statistical investigation or probability activity undertaken by others by considering features of the investigation. These features include the appropriateness of sampling methods (for example number, representativeness), quality of the data collection (for example questions asked, accuracy of measurement, fairness of the experiment), choices of measures (types of questions, and responses allowed), data analysis (technology use, choice of displays) and the extent to which claims made are supported by the evidence.

S4-4: 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%.

S4-3: 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, for example 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, for example different samples of 100 people will have different proportions.

S3-3: 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, for example the chance 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, for example March 2008 is likely to be different from March 2009.