Statistics
Core concepts
Distinguish populations from samples, parameters from statistics, and descriptive from inferential methods. Know measures of centre and spread, including mean, median, variance, and standard deviation, and how outliers and skew affect them. Understand the normal distribution, standardisation (z=\frac{x-\mu}{\sigma}), and probabilities from tables or technology. In Specialist contexts, be comfortable with the binomial distribution, expected value and variance formulas, sampling distributions, and the idea of a confidence interval for a mean.
Traps
Use (n-1) for sample variance but (n) for population variance, and do not mix the two. Remember that standardising changes location and scale, not shape, and that normal tables give cumulative areas to the left. Continuity corrections matter when approximating discrete data. Watch for confusing (P(A\cap B)) with (P(A\cup B)), and check independence assumptions before multiplying probabilities.
Worked example
If (X\sim N(50,16)), find (P(X>58)). Here (\sigma=4), so (z=\frac{58-50}{4}=2), giving (P(Z>2)\approx0.0228). Rule of thumb: standardise, sketch, then read the correct tail.
Exam strategy
State assumptions, define notation, and interpret results in context rather than reporting bare numbers.