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Statistics & Probability
Summarise data honestly: mean, median, mode, variance and standard deviation, each computed in the open. Counting principles and combinations feed straight into probability.
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Introductory
Sampling and data
Populations and samples, kinds of data, how a sample can mislead.
mean of 4, 8, 15, 16, 23, 42
Introductory
Describing data with graphs
Stemplots, histograms, box plots — and the quartiles behind them.
median of 3, 1, 4, 1, 5, 9, 2, 6
Introductory
Mean, median and mode
Centre and spread: mean, median, mode, range, variance, standard deviation.
stats 2, 4, 4, 4, 5, 5, 7, 9
Core
Probability
Events, complements, independence, the addition and multiplication rules.
1/6 * 1/6
Core
Counting: permutations and combinations
Factorials, ordered and unordered selections.
5 choose 2
Core
Discrete random variables
Probability distributions, expected value, and the binomial, geometric and Poisson families.
10 choose 3 * (1/2)^3 * (1/2)^7
Core
Continuous random variables
Density functions: probability is area, and the uniform and exponential distributions.
integrate 1/10 dx from 2 to 5
Core
The normal distribution
The bell curve, z-scores, and the 68–95–99.7 rule.
integrate e^(-x^2/2)/sqrt(2*pi) dx from -1 to 1
Core
The central limit theorem
Why averages are normal: the sampling distribution of the mean.
10/sqrt(25)
Core
Confidence intervals
Estimate ± margin of error, and what “95% confident” actually claims.
50 + 1.96*10/sqrt(100)
Core
Hypothesis testing
Null and alternative hypotheses, test statistics, p-values, and the two kinds of error.
(52 - 50)/(10/sqrt(25))
Advanced
Comparing two samples
Differences of means and proportions, and paired samples.
sqrt(4^2/20 + 3^2/25)
Advanced
Chi-square tests
Goodness of fit, independence and homogeneity: comparing observed counts with expected ones.
(20-25)^2/25 + (30-25)^2/25
Core
Linear regression and correlation
The least-squares line, the correlation coefficient, and prediction.
line through (1,2) and (3,6)
Advanced
ANOVA and the F distribution
Comparing several means at once by comparing variances.
variance of 2, 4, 4, 4, 5, 5, 7, 9
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