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Random Sampling

A sample is a slice of a population you actually study. Good conclusions require a sample that represents the whole, which is why the sampling method matters.

The main methods — simple random, systematic, stratified, and cluster — differ in how they pick members. Recognizing each from a description is the goal here.

The main methods

Simple random gives everyone an equal chance. Systematic picks every kkth member — every 25th item off a line. Stratified splits the population into groups and samples each group.

Cluster sampling picks whole pre-existing groups at random and studies everyone in them. Each method aims for representativeness in a different way.

Spotting the method

Read for the selection rule. 'Every 25th' signals systematic; 'divided by grade, then sampled' signals stratified.

'Randomly chose three whole classrooms' signals cluster; 'names drawn from a hat' signals simple random.

Worked examples

Example 1: identify the method

An inspector tests every 25th bulb off an assembly line. Which sampling method is this?

Selecting at a fixed intervalevery 25th\text{every } 25\text{th}
That is systematicsystematic sampling\text{systematic sampling}

Answer: Systematic sampling

Example 2: stratified

A school samples 10 students from each grade. Which method is that?

Split into groups, sample eachby grade\text{by grade}

Answer: Stratified sampling

Example 3: cluster

A researcher randomly picks three whole classrooms and surveys every student in them. Which method is that?

Whole groups chosen at random3 classrooms\text{3 classrooms}
Everyone inside those groups is studiedcluster sampling\text{cluster sampling}

Answer: Cluster sampling

Try one yourself

Common questions

What makes a sample representative?

It reflects the population's makeup, so conclusions about the sample carry over to the whole. Random selection helps avoid bias.

What is systematic sampling?

Selecting every kkth member from an ordered list — like every 25th item — after a random start.

How is stratified different from cluster?

Stratified samples from every group; cluster picks a few whole groups and studies all their members.

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