Data Analysis, Probability and Statistics
What you must understand
This domain combines univariate and bivariate data analysis with probability. Candidates must interpret numerical summaries (mean, median, mode, range, interquartile range, standard deviation), read and construct boxplots, histograms, dot plots and stem plots, and describe distributions in terms of shape, centre, spread and outliers. For bivariate data, you need scatterplots, the correlation coefficient r, the least-squares regression line, and interpretation of the slope and intercept in context. Probability topics include sample spaces, Venn diagrams, two-way tables, tree diagrams, conditional probability, independence, mutually exclusive events, and discrete random variables with mean and variance.
Traps that appear
- Confusing correlation with causation, or over-extrapolating a regression line beyond the data range.
- Using the mean and standard deviation for skewed data where median and IQR are more appropriate.
- Mixing up P(A|B) with P(B|A) in conditional probability questions.
- Forgetting to subtract the overlap in the addition rule P(A ∪ B) = P(A) + P(B) − P(A ∩ B).
- Assuming independence without checking P(A ∩ B) = P(A)P(B).
- Reporting r without its sign or misreading a strong negative correlation as weak.
Worked example
In a class, 60% of students study Biology, 50% study Chemistry, and 30% study both. Find the probability a randomly chosen student studies at least one. By the addition rule: P(B ∪ C) = 0.6 + 0.5 − 0.3 = 0.8. Rule of thumb: draw a Venn diagram, place the intersection first, then fill in each region by subtraction - this prevents double counting.