Statistics, data and evidence · Methods and tools

Can a larger set of data ever give less reliable knowledge than a smaller one?

It seems obvious that more data means better knowledge. Statistics teaches that how data is collected can matter more than how much there is. This question asks how sampling shapes what data can tell us.

Claims

A small random sample can represent a population well, while a huge biased sample repeats its bias with false confidence.
Statistical theory lets us state how uncertain a well-designed sample is, which is itself knowledge.

Counterclaims

With very large data sets, some biases can be detected and corrected, so size is still valuable.
Truly random samples are rare in practice, so the choice is often between different kinds of imperfect data.

Real-life situations from mathematics

The 1936 Literary Digest poll

The magazine collected about 2.4 million replies and predicted that Alf Landon would beat Franklin Roosevelt in the US presidential election. Roosevelt won by a landslide. George Gallup's far smaller but better-chosen sample called the result correctly.

Online surveys

Surveys anyone can answer online attract people with strong views and spare time, so their results can be misleading however many people respond.

Check dates and figures in a reliable source before you use them, and cite that source.

Use this in your TOK work

Essay. Fits titles about evidence, quantity versus quality, or how we know about large groups.

Exhibition. A survey form from a website or a magazine is an everyday object for a prompt about how knowledge is collected.

Link it to the prescribed title or the exhibition prompt you are working on, in your own words. See using maths examples in your essay and choosing exhibition objects.

Themes and study heading

Knowledge and politics Knowledge and technology Methods and tools

How mathematical knowledge is produced and justified.