Describe data, reason under uncertainty and test hypotheses — essential for science and data work.
Summarise data with central tendency (mean, median, mode) and spread (range, variance, standard deviation). The mean is sensitive to outliers; the median is robust. Standard deviation σ = √(Σ(x−μ)²/N) measures typical distance from the mean.
Probability ranges from 0 to 1. For independent events, P(A and B) = P(A)·P(B); for mutually exclusive events, P(A or B) = P(A)+P(B). Conditional probability P(A|B) = P(A∩B)/P(B) leads to Bayes' theorem.
The normal distribution (bell curve) describes many natural measurements; ~68% of data lies within 1σ, 95% within 2σ. The binomial models counts of successes; the Poisson models rare events over time.
We estimate population parameters from samples. A confidence interval gives a plausible range; a hypothesis test compares a null hypothesis against evidence using a p-value. A small p-value (e.g. < 0.05) suggests the result is unlikely by chance alone — but is not proof.
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