Standard Statistical analysis – Data analysis

This lesson comprises three (3) master classes focusing on:

• Data collection methods
• Classifying and organising data
• Data spread and central tendency
• Data interpretation and communication

Content:

MS-S1.1

• Describe and use appropriate data collection methods for a population or samples
  • investigate whether a sample obtained from a population may or may not be representative of the population by considering different kinds of sampling methods: systematic sampling, self-selected sampling, capture-recapture, simple random sampling and stratified sampling
  • investigate the advantages and disadvantages of each type of sampling
  • describe the potential faults in the design and practicalities of data collection processes, eg surveys, experiments and observational studies, misunderstandings and misrepresentations, including examples from the media
• Classify data relating to a single random variable
  • classify a categorical variable as either ordinal, eg income level (low, medium, high) or nominal, eg place of birth (Australia, overseas)
  • classify a numerical variable as either discrete, eg the number of rooms in a house, or continuous, eg the temperature in degrees Celsius
• Review how to organise and display data into appropriate tabular and/or graphical representations
  • display categorical data in tables and, as appropriate, in both bar charts or Pareto charts
  • display numerical data as frequency distribution tables and histograms, cumulative frequency distribution tables and graphs, dot plots and stem and leaf plots (including back-to-back where comparing two datasets)
  • construct and interpret tables and graphs related to real-world contexts, including: motor vehicle safety including driver behaviour, accident statistics, blood alcohol content over time, running costs of a motor vehicle, costs of purchase and insurance, vehicle depreciation, rainfall, hourly temperature, household and personal water usage
• Interpret and compare data by considering it in tabular and/or graphical representations
  • choose appropriate tabular and/or graphical representations to enable comparisons
  • compare the suitability of different methods of data presentation in real-world contexts, including their visual appeal, eg a heat map to illustrate climate change data or the median house prices across suburbs

MS-S1.2

• Describe the distinguishing features of a population and sample
  • define notations associated with population values (parameters) and sample-based estimates (statistics), including population mean \( \mu \), population standard deviation \( \sigma \), sample mean \( \bar{x} \) and sample standard deviation \( s \)
• Summarise and interpret grouped and ungrouped data through appropriate graphs and summary statistics
  • discuss the mode and determine where possible
  • calculate measures of central tendency, including the arithmetic mean and the median
  • investigate the suitability of measures of central tendency in real-world contexts and use them to compare datasets
  • calculate measures of spread including the range, quantiles (including quartiles, deciles and percentiles), interquartile range (IQR) and standard deviation (calculations for standard deviation only required using technology)
• Investigate and describe the effect of outliers on summary statistics
  • use different approaches for identifying outliers, including consideration of the distance from the mean or median, or the use of \( Q_1−1.5×IQR \) and \( Q_3+1.5×IQR \) as criteria, recognising and justifying when each approach is appropriate
  • investigate and recognise the effect of outliers on the mean and median
• Investigate real-world examples from the media illustrating appropriate and inappropriate uses or misuses of measures of central tendency and spread
• Describe, compare and interpret the distributions of graphical displays and/or numerical datasets and report findings in a systematic and concise manner
  • identify modality (unimodal, bimodal or multimodal)
  • identify shape (symmetric or positively or negatively skewed)
  • identify central tendency, spread and outliers, using and justifying appropriate criteria
  • calculate measures of central tendency or measures of spread where appropriate
• Construct and compare parallel box-plots
  • complete a five-number summary for different datasets
  • compare groups in terms of central tendency (median), spread (IQR and range) and outliers (using appropriate criteria)
  • interpret and communicate the differences observed between parallel box-plots in the context of the data