- Mathematics General
- Year 12
Data Analysis
approx. 7 hrs
23 topics
51 concepts
Enrol in Data Analysis to master statistical techniques and analysis.
approx. 7 hrs
23 topics
51 concepts
Enrol in Data Analysis to master statistical techniques and analysis.
In Data Analysis, students will investigate the associations between variables through data displays including plots, histograms and the use of log base 10 scale. Students will gain conceptual understanding of the normal distribution, solving problems applying the empirical rule. We will help students gain proficiency with bivariate data analysis through investigation of practical problems. Students will learn to effectively use the Pearson correlation coefficient to analyse association and causation between two variables. Data transformations of non-linear relationships using square, log or reciprocal transformations will also be explored.
This learning program is made up of the following 23 topics, broken down into 51 concepts.
Recognise variables as categorical or numerical (discrete or continuous)
Classification of categorical data as either nominal or ordinal
Construct dot plots
Interpret dot plots
Construct stem-and-leaf plots
Interpret stem-and-leaf plots
Display data in double (back-to-back) stem-and-leaf plots
Construct a frequency table including percentage frequencies
Constructing a bar and percentage bar chart from a frequency table
Interpreting and describing frequency tables and bar charts
Construct a frequency for grouped data including percentage frequencies
Construct a frequency histogram using a CAS calculator
Construct a frequency histogram
Evaluate a logarithm giving a positive or negative value
Use a CAS calculator to evaluate a number if a log is known
Use a CAS calculator to find logs
Construct a histogram with a log scale
Compare location and spread of data distributions
Describe the shape of a distribution including skewness and modes
Rounding of whole numbers and decimals to significant figures
Finding the Median From a Frequency Distribution Table
Finding the Mean From a Frequency Distribution Table
Finding the Mode From a Frequency Distribution Table
Calculate standard deviation step-by-step using the formula
Calculate the range of ungrouped data sets
Calculate Interquartile Range
Use the CAS calculator to calculate summary statistics
Construct a box plot include fencing by identifying outliers
Use the criteria to define an outlier to solve problems
Calculate the z-score from a normal distribution and interpret the results in terms of the standard deviation
Use calculated z-scores to compare scores from different data sets
Apply the empirical rule and z-scores
Use the 68-95-99.7% rule for data one, two and three standard deviations from the mean in practical situations
Implement the statistical investigation process to answer questions
Identify independent and dependent variables in bivariate data analysis
Identify and describe associations between two categorical variables from a two-way table
Use box plots, dot plots and stem plots to identify and describe associations between a numerical and a categorical variable
Construct a scatterplot using technology
Construct a scatterplot using technology
Interpret scatterplots including direction, form and strength
Calculate the coefficient of determination and interpret its value
Calculate Pearson's correlation coefficient using technology
Demonstrate understanding of correlation and causation
Classify the correlation coefficient from a scatterplot or given a value for r
Fitting a least squares line and calculating the correlation coefficient
Interpolation and extrapolation of regression lines
Find the equation of the least-squares line of best fit
Interpret the slope and intercept of a regression line
Use a residual plot to determine the appropriateness of using the equation of the least squares line to model the association
Calculate residuals
Apply the correct quadratic, logarithmic or recipricol transformation and make predictions
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