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ScotlandStatistics

Data Analysis and Modelling

6 dot points across 6 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you measure and model the linear relationship between two variables?

Analyse bivariate data using scatter plots, the sums of squares and products, the product-moment correlation coefficient, and the least-squares regression line, and assess the model with residual plots and the limitations of extrapolation.
A focused answer to the SQA Advanced Higher Statistics bivariate data content: scatter plots, the sums of squares Sxx, Syy and Sxy, the product-moment correlation coefficient, the least-squares regression line, prediction, residual plots and the dangers of extrapolation.
13 min answer →

How do you model a continuous measurement, and how do you find probabilities from a normal distribution?

Work with continuous random variables and the normal distribution, standardise to find probabilities, combine independent normal variables, and use the normal approximation to the binomial and Poisson distributions with a continuity correction.
A focused answer to the SQA Advanced Higher Statistics continuous random variables content: the normal distribution, standardising to the Z-distribution, finding probabilities and quantiles, combining independent normal variables, and the normal approximation to the binomial and Poisson with a continuity correction.
13 min answer →

How do you model a count with a discrete random variable and find its expected value and variance?

Work with discrete probability distributions, calculate the expectation and variance of a discrete random variable and apply the laws of expectation and variance, and use the binomial, Poisson and geometric distributions as models.
A focused answer to the SQA Advanced Higher Statistics discrete random variables content: probability distributions, the expectation and variance of a discrete random variable, the laws of expectation and variance, and the binomial, Poisson and geometric distributions with their means and variances.
13 min answer →

How do you design a study and collect data so that the conclusions you draw are valid and free from bias?

Describe the principles of experimental design, distinguish observational studies from designed experiments, identify sources of bias, and explain control, randomisation, replication and blocking when planning data collection.
A focused answer to the SQA Advanced Higher Statistics experimental design content: the difference between observational studies and designed experiments, control, randomisation, replication and blocking, the types of variable, and the common sources of bias that invalidate conclusions.
11 min answer →

How do you summarise and display a data set so its centre, spread and shape are clear?

Calculate and interpret measures of location and dispersion, including the mean, median, quartiles, interquartile range, variance and standard deviation, and use stem-and-leaf plots, boxplots and measures of skewness to describe the shape of a distribution.
A focused answer to the SQA Advanced Higher Statistics exploratory data analysis content: the mean, median and quartiles, the interquartile range, variance and standard deviation, stem-and-leaf plots and boxplots, outlier rules, and how to describe the shape and skewness of a distribution.
12 min answer →

How do you calculate probabilities for combined, conditional and independent events?

Apply the addition and multiplication laws of probability, calculate conditional probabilities and use tree diagrams, the total probability rule and Bayes' theorem, and test events for independence and mutual exclusivity.
A focused answer to the SQA Advanced Higher Statistics probability content: the addition and multiplication laws, conditional probability, independence and mutual exclusivity, tree diagrams, the total probability rule and Bayes' theorem for reversing a conditional probability.
12 min answer →