- MST-11-08 displays and analyses datasets using summary statistics and graphical representations
📖 Prior Knowledge
| Content | Prerequisite relationships |
|---|---|
| Data A | - Design a survey to collect data (revisited content) - Construct column graphs with a many-to-one scale → Represent data with a variety of graphs - Interpret tables, column graphs and line graphs → Interpret graphs to draw conclusions |
| Data B | - Compare data displays by range and mode → Compare datasets using measures - Identify misleading data representations → Explain misleading graphs |
| Fractions Decimals Percentages | - Find a percentage of a quantity → Represent data with a variety of graphs |
| Data Classification and Visualisation | - Define a statistical variable → Classify variables as numerical or categorical - Classify variables as numerical or categorical (revisited content) - Describe data subtypes (revisited content) - Represent data with a variety of graphs (revisited content) - Choose and justify a graph type (revisited content) - Interpret graphs to draw conclusions (revisited content) - Explain misleading graphs (revisited content) |
| Data Analysis | - Calculate mean, median, mode and range (revisited content) - Find summary statistics from a frequency table (revisited content) - Compare datasets using measures (revisited content) - Identify clusters, gaps and outliers (revisited content) - Explain effects on measures of centre (revisited content) - Choose the most appropriate measure of centre (revisited content) - Describe the shape of a distribution (revisited content) - Distinguish a census from a sample → Evaluate sampling methods and sample size |
| Data Analysis A | - Calculate and compare standard deviation (revisited content) - Determine the 5-number summary (revisited content) - Determine the five-number summary from a display → Determine quartiles from a cumulative histogram - Determine quartiles from a cumulative histogram (revisited content) - Determine the interquartile range (revisited content) - Represent data using box plots (revisited content) - Find proportions and counts from a box plot (revisited content) - Compare datasets using box plots (revisited content) - Identify skewness from displays (revisited content) |
| Data Analysis C | - Evaluate sampling methods and sample size (revisited content) |
Statistical investigation process
- Identify an issue and pose a question to a targeted population to gather statistical information
- Develop a survey by applying questionnaire design principles of clear language, unambiguous questions and consideration of number of choices
- Examine issues of privacy, bias, ethics and responsiveness to diverse groups and cultures
Population and sample
- Compare and contrast systematic sampling, self-selected sampling, random sampling and stratified sampling
- Justify whether a sample obtained from a population is representative of the population by considering the sampling method
- Describe the potential faults in the design and practicalities of a data collection process by considering survey design, experiments and observational studies, and misunderstandings and misrepresentations
Data classification
- Classify and describe variables as numerical or categorical
- Describe a numerical variable as discrete or continuous
- Describe a categorical variable as nominal or ordinal
- Identify collections of data that can be described as numerical or categorical depending on responses
Display and interpret grouped and ungrouped data
- Recognise and explain why some datasets need to be grouped to allow for appropriate representation and analysis
- Use a spreadsheet to organise and represent data using appropriate graphs
- Represent a numerical dataset as either a frequency distribution table or a cumulative frequency distribution table and graph the associated histogram with polygon, both with and without using digital tools
- Represent categorical datasets in tables and column graphs as appropriate, with and without using digital tools
- Select the type of graph best suited to represent various single datasets and justify the choice of graph
- Identify and describe the shape of the distribution of a dataset as either symmetric, positively skewed or negatively skewed
- Interpret and analyse dot plots, line graphs, sector graphs, stem-and-leaf plots, back-to-back stem-and-leaf plots and divided bar charts related to real-world applications
- Analyse a statistical infographic and justify the choice of graphical representations used for the relevant dataset
- Interpret and consider limitations of graphical representations to make conclusions and predictions
- Explain why a given graphical representation can lead to a misinterpretation of data
Measures of centre and spread
- Describe the mean, median and mode as measures of centre and calculate their values for a dataset in graphical form and tabular form, using a scientific calculator and other digital tools
- Identify and describe datasets as uniform, unimodal, bimodal or multimodal
- Identify the range and standard deviation as measures of spread to describe variation in a dataset
- Calculate the range and population standard deviation of a dataset using a scientific calculator or other digital tools
- Compare datasets using measures of centre and measures of spread
- Examine the merits of each measure of centre and justify where each measure is most appropriately used
- Identify and describe real-world examples illustrating appropriate and inappropriate uses of measures of centre and measures of spread
- Use a spreadsheet to analyse data including calculating measures of centre and spread
Quartiles and interquartile range
- Determine the five-number summary from a set of numerical data or graphical representation
- Determine the interquartile range (IQR) of datasets
- Compare and contrast the use of range and IQR as measures of spread
Five-number summary and box plots
- Represent numerical datasets using a box plot to display a five-number summary, with and without using digital tools
- Compare and contrast the measures of centre, spread and shape using parallel box plots
- Determine quartiles from datasets displayed in histograms and dot plots, and represent these datasets as a box plot
- Interpret box plots to draw conclusions and make inferences about a dataset
Clusters and outliers
- Identify clusters, gaps and outliers and explain their occurrence in the context of the data
- Apply and to formally identify outliers
- Explain the impact of outliers on the measures of centre and spread