- Mathematics General
- Year 12
Data and Statistics
approx. 25 hrs
8 topics
75 concepts
Develop strong mathematical skills in Data and Statistics to approach your examinations with confidence.
approx. 25 hrs
8 topics
75 concepts
Develop strong mathematical skills in Data and Statistics to approach your examinations with confidence.
The Year 12 Data and Statistics program is aligned to the outcomes from the Statistics and Probability Strand in the Australian curriculum. In Data and Statistics, students study statistical processes and inquiry in society, acquire skills in statistical techniques to display and interpret small and large data sets, and apply reasoning in the evaluation and construction of arguments and the interpretation and use of models based on statistical concepts.
This learning program is made up of the following 8 topics, broken down into 75 concepts.
Creating and evaluating questions as part of the statistical inquiry
Identify and select different sampling techniques - simple random, systematic and stratified
Calculate how to obtain a systematic sample
Calculate proportions from a stratified sample
Identify the target population - census or sample
Describe the process of a statistical investigation
Interpret a histogram with a log scale
Construct frequency histogram and polygon for grouped data
Construct a histogram with a log scale
Divide large sets of data into percentiles
Divide large sets of data into quartiles
Analyse a variety of data displays
Identify and analyse misleading graphs
Identify and explain which graph types are suitable for the type of data being considered
Construct Frequency Distribution Tables: Grouped Data
Construct frequency tables for grouped data from cumulative frequency graphs
Determine logs from numbers
Determine numbers from logs
Read percentiles from graphs
Divide large sets of data into deciles
Read quartiles from graphs
Interpret a radar chart
Construct a radar chart
Read deciles from graphs
Use a residual plot to determine the appropriateness of using the equation of the least squares line to model the association
Calculate residuals
Construct the least-squares line of best fit
Find the equation of the least-squares line of best fit
Demonstrate understanding of correlation and causation
Interpret the slope and intercept of a regression line
Find the equation of a line of best fit
Use a line of best fit to make predictions of data sets
Draw a line of best fit on a scatterplot
Classify the correlation coefficient from a scatterplot or given a value for r
Construct scatterplots
Interpret scatterplots including direction, form and strength
Fit a least-squares line to a time series plot and make predictions
Identify key features in a time series plot
Smoothing a time series plot using moving means
Smoothing a time series plot using moving medians
Describing time series plots by identifying key features
Construct time series plots
Calculate seasonal indices
Interpret seasonal indices
Deseasonalise data
Reseasonalise data
Determine the five-number summary from a stem-and-leaf plot
compare summary statistics, including mean, mode, median, and population standard deviation, for two sets of data
Estimate the upper and lower quartiles of a data set from a cumulative frequency polygon for grouped data
Estimate the median of a data set from a cumulative frequency polygon for grouped data
Establish a five-number summary for a data set
Calculate Interquartile Range
Calculate the range of ungrouped data sets
Construct a box plot using the five-number summary
Identify outliers and describe the impact on the measures of centre and spread
select and use the appropriate statistic (mean, median or mode) to describe features of a data set
Estimate the median From a cumulative frequency graph
Compare summary statistics from a variety of contexts including measures of centre and measures of spread
Finding the Standard Deviation on a Calculator
Finding the Mean on a Calculator
Finding the Mode From a Frequency Distribution Table
Finding the Mean From a Frequency Distribution Table
display two sets of data on a radar chart
determine the percentages of data between any two quartiles on a box-and-whisker plot
prepare an area chart to illustrate and compare different sets of data over time
Use two-way tables to calculate probabilities
display data in two box-and-whisker plots drawn on the same scale
display data in double (back-to-back) stem-and-leaf plots
Describe the shape of a distribution including skewness and modes
Calculate the standardised value, called the z-score, of a normal distribution
use calculated z-scores to compare scores from different data sets
verify that the mean of the distribution of all possible sample means is equal to the population mean for populations
use the capture/recapture technique for estimating the size of populations
recognise the effect of sample size in estimating the nature of a population
apply counting techniques to list all possible samples of varying sizes from a known small population
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