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ScotlandApplications of Mathematics

Statistics and Probability

4 dot points across 4 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you measure how strongly two variables are related, and use a line of best fit to predict?

Measuring linear association with Pearson's correlation coefficient, fitting a simple linear regression line, interpreting its slope and intercept, and using it to predict while distinguishing interpolation from extrapolation.
A focused answer to the SQA Higher Applications of Mathematics content on correlation and regression, covering Pearson's r, the strength and direction of association, the least-squares regression line, interpreting slope and intercept, prediction, and correlation versus causation.
9 min answer →

How do you test a claim about data and estimate a population value with a confidence interval?

Carrying out and interpreting hypothesis tests (t-tests and z-tests), using the p-value and significance level to reach a conclusion, constructing and interpreting confidence intervals, and recognising errors in statistical testing.
A focused answer to the SQA Higher Applications of Mathematics inferential statistics content, covering null and alternative hypotheses, p-values and significance levels, t-tests and z-tests, confidence intervals, and errors in statistical testing.
10 min answer →

How do you calculate probabilities of combined events and the expected value of an uncertain outcome?

Calculating probabilities of single and combined events using the addition and multiplication rules and tree diagrams, working with conditional probability, and finding the expected value of a situation with uncertain outcomes.
A focused answer to the SQA Higher Applications of Mathematics probability content, covering basic probability, combining events with the addition and multiplication rules, tree diagrams, conditional probability, and calculating expected value.
9 min answer →

How do you choose, draw and read statistical diagrams, and sample data without bias?

Selecting and interpreting statistical diagrams, comparing data sets using measures of centre and spread, identifying outliers and misleading graphs, and choosing an appropriate sampling method.
A focused answer to the SQA Higher Applications of Mathematics content on statistical diagrams and sampling, covering box plots and histograms, comparing distributions, outliers, misleading graphs, data types, and sampling methods.
9 min answer →