# Probability and Statistics

Probability and statistics are two branches of mathematics. Probability and statistics are highly related and are often studied together because statistical analyses often involve the use of probability distributions. There are also many aspects of probability theory that involve topics that are almost entirely mathematical.

## Probability theory

Probability theory is a discipline mainly studies random phenomena. The outcome of a random event cannot be determined before it occurs. The actual outcome is to be determined by probability or chance. In probability theory, the probability or chance is represented by a numerical value between 0 and 1 which describes how likely an event is to happen. A probability of 0 indicates that it is impossible for an event to happen while a probability of 1 means that it is sure to happen.

Example:

What is the probability to get a 5 when rolling a 6-sided dice?

For a perfectly balanced 6-sided dice, the possibility of each side showing up is the same. Therefore, the probability of getting a 5 is or 0.16667.

## Statistics

Statistics is a discipline that involves collecting, organizing, displaying, analyzing, interpreting, and presenting data. It is widely used in scientific research, when considering social problems, and for industrial purposes, among many other applications.

On a base level, it involves proper data collection through sampling if full census data cannot be collected, designing and conducting experimental and observational studies, and formulating conclusions or re-designing the studies based on the data.

Example:

The following are the test scores of 7 students in a class: 98, 78, 80, 88, 86, 92, 73. Below are a few basic statistical values using the student's test scores.

 The sum of the scores: 595 The average score: The median score: 86