# 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

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

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)