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Branches of Statistics

Statistics is broadly divided into two main sub-fields: Descriptive Statistics and Inferential Statistics.

Definition: Involves the collection, organization, analysis, interpretation, and presentation of data.
Purpose: Focuses on summarizing and describing the main features of a data set without making inferences or predictions about a larger population.
It primarily deals with the analysis of past data.
Two fundamental concepts in descriptive statistics are Measures of Central Tendency and Measures of Dispersion.

Definition: A branch of statistics where predictions or inferences are made about an entire population based on data collected from a sample.
This approach is used when it's impractical or impossible to analyze the entire population.

Population: The entire group of individuals or items that are the subject of interest (e.g., all cricket fans in India, all students enrolled in a college).
Sample: A subset of the population chosen for analysis (e.g., cricket fans who watch matches in stadiums, students who physically attend college lectures).

To ensure accurate predictions about the population, samples must adhere to three important criteria:
- Sufficient Size: The sample must be large enough to allow for proper inference.
- Randomness: Sampling should be random to avoid bias.
- Representativeness: The sample must reflect all variations present in the population (e.g., for average salary in India, include individuals from all states, genders, age groups, and economic classes).

Hypothesis Testing: Involves testing an assumption or hypothesis about a population parameter based on sample data (e.g., testing if the mean height of a population differs from a specific value).
Confidence Intervals: Used to estimate a population parameter from a sample and determine the confidence level of that estimate.
Other techniques include Regression, Chi-Square Test (for categorical variables), various Sampling Techniques, and Bayesian Statistics.