## Kolmogorov Axioms

### Introduction

Kolmogorov axioms or probability axioms were introduced by Soviet mathematician Andrey Kolmogorov(April 25, 1903- October 20, 1987).

All the theorems in probability theory are derived from the axioms.

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## σ-algebra

### Definition

σ-algebra or Borel field is a collection of subsets of a sample space S,

and it must satisfy the following three properties:

• The empty set is an element of σ-algebra.
• σ-algebra is closed under complementation.
• σ-algebra is closed under countable unions.

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## Sample Space

### Definition

Sample space is a set of all possible outcomes of an experiment.

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## Measures of Central Tendency

### Introduction

Measures of central tendency are used to describe the trend of value or values in a dataset.

### Related Topics

◆ Arithmetic Mean

◆ Geometric Mean

◆ Harmonic Mean

◆ Truncated Mean

◆ Mode

◆ Median

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## Measures of Dispersion

### Introduction

Measures of Dispersion are used to understand the scatterings of data.

### Related Topics

◆ Range

Variance

◆ Standard Deviation

◆ Coefficient of Variance

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## What is Descriptive Statistics?

### Introduction

Descriptive statistics is a study of managing and describing data properties and exchanging the data into useful information.

Related Topics

Frequency Distribution

◆ Charts

◆ Scales of Measurement

◆ Measures of Central Tendency

◆ Measures of Dispersion

◆ Skewness and Kurtosis

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