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Elaborations on Level Two: Statistics

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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:

Statistical investigation

S2-1: Conduct investigations using the statistical enquiry cycle:

  • posing and answering questions
  • gathering, sorting, and displaying category and whole-number data
  • communicating findings based on the data.

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:
 

stats cycle.

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, for example how many people live in your house? or from rounding of measures, for example 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, for example boys like outdoor games more than girls. Supporting teaching resources.

Click to download a PDF of second-tier material relating to Level 2 Statistical Investigations (584KB)

Statistical literacy

S2-2: 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, for example strip and pie graphs show proportions well, pictographs and bar graphs show differences well. Supporting teaching resources.

Probability

S2-3: 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, for example playing a game of chance, and making simple models of all the outcomes, for example lists or tables, students should recognise when outcomes appear to be equally likely, for example 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, for example "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, for example "it is very likely to rain today". Supporting teaching resources.

Click to download a PDF of second-tier material relating to Level 2 Probability (74KB)