Random sampling
You can only ask a few members of a population. How do you choose them so the few speak fairly for everyone?
Where you are 4 inside
What this area is about
When the person collecting data picks the sample, or the eager pick themselves, the result leans toward whoever was reached. Random sampling hands the choice to chance, so no one’s preferences tilt it and anyone can check it was fair. The four methods here differ in what you need in hand (a full list, known groups, an ordered line) and in what they cost.
How these fit together
The basic method. A simple random sample of n from N gives every member, and every group of n members, the same chance of being chosen. It needs a list of the whole population.
Variations that use structure. A stratified random sample splits the population into strata that answer differently and draws a simple random sample inside each, so every group gets its share. A systematic sample takes a random start and then every k-th individual, with \displaystyle k = \frac{N}{n} (rounded down when not whole), for individuals that arrive in order. A cluster sample draws whole ready-made groups at random and measures everyone in them, for when the groups can be listed but the members cannot.
A path through it
The simple random sample first. Then the systematic and stratified samples, and the cluster sample after the stratified one, since it reuses the idea of splitting into groups but draws whole groups.
Finish here and bias shows what goes wrong without chance, and sampling distributions study how a random sample’s result varies from draw to draw.