Statistics: A Guide to Data Analysis and Population Inference
Classified in Mathematics
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What is Statistics?
Statistics is a set of tools designed to analyze data and deduce information about a population from a given sample.
The Three-Step Process of Statistics
- 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.
- Descriptive Statistics: Analyze the data to get information about the sample.
- Statistical Inference: From the data, deduce information about the whole population.
Context is Crucial
The context of a statistical study is crucial in interpreting the results. 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 to study.
Choosing a Representative Sample
Choosing a sample is a delicate task: the sample must be representative of the population (context is important).
Sample Size
The size of a sample depends on the situation. Usually, a sample must have at least 30 individuals.
Sampling Strategies
When choosing a sample, there are several strategies: random sampling, stratified sampling, cluster sampling, etc.
Variables
Variables are questions that we ask the population. They should be neutral and serve a purpose. The possible answers of a variable must be clear from the beginning.
Types of Variables
- Quantitative or Numerical: The answer is a number.
- Qualitative or Categorical: The answer is a label (category).
Quantitative Variables
- Discrete: The answers are obtained by counting.
- Continuous: The answers are obtained by measuring.
Data Analysis Tools
- Frequency tables (organize the data)
- Graphic representations of data (visually represent the data)
- Descriptive statistics (measure features of the data)