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Module 9 · Sampling and Inference Module contents
Module 9  ·  Card 1 / 16beginner

Population vs Sample

A population is the whole group you want to know about, and a sample is the part of it you actually measure.

Measuring a whole population is often too slow or costly, so a well-chosen sample stands in for it.

For example, a polling firm asks 1,000 voters how they will vote to estimate the views of millions.

A number describing the population, such as its true mean, is a parameter; the same number from a sample is a statistic.

A statistic varies from sample to sample, so inference is about judging how far it might sit from the parameter.

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Module 09 · Sampling and Inference · 16 concepts
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Population vs Sample, in more detail

Almost every statistical question is about a population that cannot be measured in full.

The population might be every customer, every voter or every product made in a year.

A sample is the practical answer, and inference is the reasoning that carries findings from it back to the population.

The population must be defined precisely, such as customers who ordered in the last 12 months, not just customers.

A sample only tells you about the population it was drawn from, so a vague definition leads to vague conclusions.

Parameters are fixed but unknown, such as the true share of customers who would renew.

Statistics are known but variable, because a different sample would give a slightly different value.

Textbooks often write population values with Greek letters, such as mu for the mean, to keep them apart from sample values.

Bigger samples give statistics closer to the parameter on average, but with diminishing returns.

How the sample is chosen matters more than its size, since a biased method misleads at any size.

Sometimes the whole population is available, such as every transaction in a company's database.

Even then, the data is often treated as a sample of a wider process, such as the transactions that could happen next year.

In practice, stating the population, the sampling method and the sample size is the first line of any honest analysis.

A finding about customers in one country is not automatically true of customers in another.

The common misconception is that a large sample is automatically representative, when that comes from how it was drawn.

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Question 1
A survey of 800 shoppers finds they spend £42 on average per visit. What is the £42?
Sampling and Inference

16 concepts in this module, then a graded test with every answer explained.

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