In statistics, a population and a sample are two fundamental concepts used to describe the group of individuals or observations under study:

1. **Population**:

Definition: A population refers to the entire group of individuals, objects, or observations about which you want to make inferences or draw conclusions in a statistical study. It includes every possible member of the group of interest.

A numerical summary of a population is called Parameter.

Notation: Typically denoted as N.

2. **Sample**:

Definition: A sample is a subset of the population, selected to represent the larger population. It is used to make estimates and draw conclusions about the population, as it is often impractical or impossible to collect data from an entire population.

A numerical summary of a sample drawn from that population is called Statistic.

Notation: Typically denoted as n.

Here's a table with the formulas for various statistical metrics for both populations (denoted with subscript "N") and samples (denoted with subscript "n"):

In these formulas,

These formulas are used to calculate central tendencies, variability, and relationships between variables in both populations and samples, allowing statisticians to draw meaningful conclusions from data.