Critical Approach to Statistics - Progression Points

Dimension

Level

Progression Point

Measurement, chance and data

1.75

• Collection and recording of categorical and numerical data

2.0 Standard

… Students collect simple categorical and numerical data (count of frequency) and present this data using pictographs and simple bar graphs.

2.75

• Understanding of the distinction between discrete and continuous scales

3.0 Standard

… Students recognise different types of data: non-numerical (categories), separate numbers (discrete), or points on an unbroken number line (continuous).

They use a column or bar graph to display the results of an experiment (for example, the frequencies of possible categories).

3.25

• Identification of mode and range for a set of data

3.5

• Design of questionnaires to obtain data from a sample of the population
  
  
• Sorting of data using technology

3.75

• Calculation and analysis of the stability of a sequence of long run frequencies where the number of trials increases, for example from 5 to 10 to 20 to 100
• Interpretation of pie charts and histograms
• Identification of the median for a set of data

4.0 Standard

… Students recognise and give consideration to different data types in forming questionnaires and sampling.

They distinguish between categorical and numerical data and classify numerical data as discrete (from counting) or continuous (from measurement).

They calculate and interpret measures of centrality (mean, median, and mode) and data spread (range).

4.25

• Recognition of the mean value of a set of measurements as the best estimate, and that the range could represent the associated error

4.5

• Contrast between the stability of long run relative frequency and the variation of observations based on small samples

4.75

• Display and interpretation of dot plots, and stem and leaf plots, including reference to mean, median and mode as measures of centre

5.0 Standard

… Students organise, tabulate and display discrete and continuous data (grouped and ungrouped) using technology for larger data sets.

They represent uni-variate data in appropriate graphical forms including dot plots, stem and leaf plots, column graphs, bar charts and histograms.

They calculate summary statistics for measures of centre (mean, median, mode) and spread (range, and mean absolute difference), and make simple inferences based on this data.

5.25

• Representation of statistical data using technology

5.5

• Display of data as a box plot including calculation of quartiles and inter-quartile range and the identification of outliers

6.0 Standard

Students comprehend the difference between a population and a sample.

They calculate summary statistics for centrality (mode, median and mean), spread (box plot, inter-quartile range, outliers) and association (by-eye estimation of the line of best fit from a scatter plot).

They distinguish informally between association and causal relationship in bi-variate data, and make predictions based on an estimated line of best fit for scatter-plot data with strong association between two variables.