# Purpose and content of

Classified in Mathematics

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Statistics is a set of tools designed to analyze data and deduce information about a population
from a given sample.
What is Statistics?
• It is a three‐steps process:
1. Sampling and design of the experiment: take a sample (or many) from the population, make
observations about the sample, and turn them into numerical data.
2. Descriptive statistics: analyze the data to get information about the sample.
3. Statistical inference: from the data, deduce information about the whole population.
• Context is crucial in this process
A population is a set of individuals (people, cases, etc) that we want to analyze.
A sample is a subset of the population.
A variable is an aspect or characteristic of the population that we want study.
Choosing a sample is a delicate task: the sample must be representative of the population (context
is important).
• How big should a sample be? Clearly, it will depend on the situation. Usually, a sample must have
at least 30 individuals.
When choosing a sample, there are several strategies: random sampling, stratified sampling,
cluster sampling, etc
The variables are just questions that we ask the population.
The variables should be neutral:
• Are you in favor of the illegal one‐sided declaration of independence of the autonomous region of
Catalunya from the great Spanish nation?
• Are you in favor of the historically legitimated declaration of independence of the great nation of
Catalunya from the oppressive Spanish state?
• The variables must serve a purpose: if I am interested in the income per family, is it necessary to
• The possible answers of a variable must be very clear from the beginning.
• There are two types of variables, depending on the kind of answer: • Quantitative or numerical: