Populations and samples

In statistics, we aim to understand large groups (populations) by studying smaller, manageable subsets known as samples. The data we collect from these samples is summarised using statistics, which help us describe key features of the sample. These statistics then serve as estimates of the true values, called parameters, that describe the entire population. 

This section introduces these foundational concepts and explains how they connect in practical data analysis.

1. Population

Experiments such as exit polls or comparison of groups that were in the previous step are limited to generating data only about available ‘subjects’. But we are actually interested in obtaining information about a total collection of all subjects referred to as the population.

In the previous examples, the population would be the total electorate of 10 million voters, or the entire population of students undertaking computer programming learning, respectively.

In other examples, this could be all the residents of a city, or all the television sets produced in the last year by a particular manufacturer, or all the households in a community.

2. Sample

Because the population is often too large to examine each of its members, we try to learn about it by choosing and examining a subgroup of its elements, called a sample.

3. Statistic

The data obtained in the sample is analysed using various summaries that capture its key features.

For instance, this could be:

• An observed relative frequency (percentage) of a certain response in an opinion poll.
• The arithmetic average of collected measurements in a repeated physical experiment.
• The most popular UK movie of 2023 as selected by a focus group of viewers.

Any such summary or, more generally, a function of the ‘sample data’ is called a statistic.

4. Parameter and estimate

The corresponding summary value for the entire ‘population’ is called a parameter, and the sample statistic at hand may be thought of as an estimate of that parameter.

In the situations listed in previous the 3. Statistic section, the population parameter of interest would be:

• The proportion in the general population of voters holding a particular view.
• The ‘true’ value of the physical measurement.
• The most popular movie in the entire population of UK viewers.