📊 Inferential Statistics

Last Updated: Jan 2026

Inferential Statistics is the branch of statistics used to draw conclusions about a population using sample data.

Instead of analyzing the whole population, we:

  • Take a sample
  • Analyze it
  • Make predictions or decisions about the population

Because:

  • Population data is often too large
  • Collecting all data is costly or impossible
  • Decisions must be made using limited data

🗣 Hinglish Tip: Inferential statistics = sample dekh ke population ka andaza lagana

Population

Population is the entire group you want to study.

Examples

  • All students in a country
  • All customers of a company
  • All transactions in a year

Notation

  • Population size → N
  • Population mean → μ
  • Population variance → σ²

🗣 Hinglish Tip: Population = poora data, jitna exist karta hai

Sample

Sample is a subset of the population used for analysis.

Examples

  • 1,000 students from all students
  • 500 customers from all users

Notation

  • Sample size → n
  • Sample mean → x̄
  • Sample variance → s²

🗣 Hinglish Tip: Sample = population ka chhota hissa

Sampling Techniques

Sampling is the process of selecting a sample from a population.

Goal:

  • Sample should represent the population
  • Results should be unbiased

Sampling techniques are divided into two main types:

  1. Probability Sampling
  2. Non-Probability Sampling

Probability Sampling

Every element of population has a known and non-zero chance of being selected.

Simple Random Sampling

  • Every member has equal chance
  • Uses random numbers

Example:

  • Lottery method

🗣 Hinglish Tip: Simple random = luck based selection

Systematic Sampling

  • Select every kth element

Formula:

k = N / n

Example:

  • Every 10th customer

Stratified Sampling

  • Population divided into groups
  • Sample taken from each group

Example:

  • Students grouped by class
  • Employees grouped by department

🗣 Hinglish Tip: Stratified = har group se thoda-thoda data

Cluster Sampling

  • Population divided into clusters
  • Entire clusters are selected randomly

Example:

  • Selecting some schools and surveying all students in them

Non-Probability Sampling

Selection is not random. Chance of selection is unknown.

Convenience Sampling

  • Easily available data

Example:

  • Friends, nearby people

Judgmental (Purposive) Sampling

  • Researcher selects based on judgment

Example:

  • Expert opinions

Quota Sampling

  • Fixed number from each category

Example:

  • 50 males, 50 females
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