Statistics and probability are two interrelated fields of mathematics that deal with analyzing data and making inferences about populations or phenomena based on sample data.

Statistics

Statistics is the science of collecting, analyzing, interpreting, presenting, and organizing data. It provides tools and methodologies for understanding data and making informed decisions based on statistical analysis. Here are some key components of statistics:

1. Descriptive Statistics: This branch deals with summarizing and organizing data. Common descriptive statistics include:

   • Measures of Central Tendency: Mean (average), median (middle value), and mode (most frequent value).
   • Measures of Dispersion: Range, variance, and standard deviation, which indicate how spread out the data is.
   • Data Visualization: Tools such as graphs, charts, and tables that help in displaying and interpreting data more easily.

2. Inferential Statistics: This branch involves making predictions or inferences about a population based on a sample. Key concepts include:

   • Hypothesis Testing: A method for testing a claim or hypothesis about a population parameter.
   • Confidence Intervals: A range of values used to estimate the true value of a population parameter with a certain level of confidence.
   • Regression Analysis: A statistical method for examining the relationship between variables.

   Statistics in Maths | Definition, Types, Formulas, and Applications

Probability

Probability in Maths | Formula, Theorems, Definition, Types, Examples

Probability

Probability refers to the extent of occurrence of events. When an event occurs like throwing a ball, picking a card from deck, etc ., then the must be some probability associated with that event.

Basic Terminologies:

• Random Event :- If the repetition of an experiment occurs several times under similar conditions, if it does not produce the same outcome everytime but the outcome in a trial is one of the several possible outcomes, then such an experiment is called random event or a probabilistic event.
• Elementary Event – The elementary event refers to the outcome of each random event performed. Whenever the random event is performed, each associated outcome is known as elementary event.
• Sample Space – Sample Space refers to the set of all possible outcomes of a random event.Example, when a coin is tossed, the possible outcomes are head and tail.
• Event – An event refers to the subset of the sample space associated with a random event.
• Occurrence of an Event – An event associated with a random event is said to occur if any one of the elementary event belonging to it is an outcome.
• Sure Event – An event associated with a random event is said to be sure event if it always occurs whenever the random event is performed.
• Impossible Event – An event associated with a random event is said to be impossible event if it never occurs whenever the random event is performed.
• Compound Event – An event associated with a random event is said to be compound event if it is the disjoint union of two or more elementary events.
• Mutually Exclusive Events – Two or more events associated with a random event are said to be mutually exclusive events if any one of the event occurs, it prevents the occurrence of all other events.This means that no two or more events can occur simultaneously at the same time.
• Exhaustive Events – Two or more events associated with a random event are said to be exhaustive events if their union is the sample space.