Statistics turns data into decisions. These guides explain how to summarise a data set, measure its spread, count outcomes and judge how unusual a value is.
Introductory statistics asks a small set of questions again and again: what is a typical value, how spread out are the values, how likely is an outcome, and how unusual is this observation? The guides in this section answer each one with a clear method and a fully worked example.
You will learn when the median describes a data set better than the mean, why sample standard deviation divides by , how to tell a permutation problem from a combination problem, and how to turn a z-score into a percentile. Each numeric result in these articles has been recomputed, and the statistics calculators show the same calculations step by step.
Statistics is also about honest reporting. A mean without a measure of spread, or a probability without its assumptions, can mislead, so each guide states clearly what its formula assumes, for example independent events or a normally distributed population, and what to do when that assumption fails.
Start with averages and standard deviation, then probability, counting, and z-scores.
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Mean, median and mode describe the centre of a data set, while range and standard deviation describe how spread out it is. Knowing how to compute each one, and when each gives an honest summary, is the foundation of statistics.
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Standard deviation measures how far data values typically lie from their mean. This guide walks through the calculation step by step, explains when to divide by n and when by n minus 1, and shows how to read the answer once you have it.
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Probability measures how likely an event is on a scale from 0 to 1. A handful of rules, for complements, unions, independent and dependent events and conditional probability, solve most problems, and knowing the classic traps prevents most mistakes.
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A z-score tells you how many standard deviations a value lies above or below the mean. It lets you compare values measured on different scales and, for normally distributed data, convert any value into a percentile or probability.
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Permutations count arrangements where order matters, and combinations count selections where it does not. Both grow from the fundamental counting principle and factorials, and they power probability calculations from card games to lotteries.