Statistics

Statistics is a discipline of mathematics that deals with all aspects of data. Statistical knowledge aids in the selection of the most appropriate method for gathering data and the proper use of those samples in the analysis process in order to provide successful results. In a nutshell, statistics is a critical process that aids in making data-driven decisions.

Statistics:

Statistics is a branch of mathematics that deals with data gathering, organization, interpretation, analysis, and presentation. The primary goal of statistics is to organize the information gathered in terms of experimental designs and statistical surveys. Statistics is a mathematical study that deals with numerical information. In a nutshell, statistics is a critical process that aids in making data-driven decisions. 

Types of Statistics:

The two primary branches of statistics are as follows:

1. Descriptive statistics
2. Inferential statistics 

Descriptive Statistics:

Descriptive statistics are used to describe something. Descriptive statistics employs data to create demographic descriptions using graphs, tables, and numerical calculations.

Inferential Statistics 

Inferential statistics generates predictions and inferences based on a sample of data obtained from the population.

In the discipline of statistical analysis, both types of statistics are used equally. 

Mean, median, and mode:

Mean:

The arithmetic average of a Data set is calculated by summing all of the numbers in the set and dividing by the number of observations in the Data set. 

Mean =  x̄ = ∑x/n

Median: 

The Median is the middle number in the data set when it is arranged in ascending or descending order.

Median = (n + 1)/2th term,  if n Is odd. 

Median = (n/2)th term + (n/2 + 1)th term / 2, if n Is even.

Mode:

The Mode is the number that appears the most in a Data set and varies from the highest to the lowest value.

The value that appears the most frequently is known as the mode.

Application of statistics:

Statistical modeling entails creating predictive models based on data development, pattern perception, and design. Modeling is commonly utilized in election outcomes prediction, population survival analysis, and scientific surveys. Meteorologists utilize these techniques to forecast the weather and investigate various environmental and geographical disturbances on the planet.

Probability:

Probability is a statistic for calculating the likelihood of an event happening. Many things are impossible to predict with absolute certainty. We can only predict the probability of an event occurring using it, i.e. how likely it is to occur. The probability scale runs from 0 to 1, with 0 indicating an unlikely event and 1 indicating a foregone conclusion.. 

The formula for Probability:

The probability formula states that the ratio of the number of favorable outcomes to the total number of alternatives equals the likelihood of an event occurring.

 Probability of an event occurring P€ = Number of positive outcomes/Total Number of positive outcomes 

Types of probabilities:

Probabilities can be divided into three categories.

1. Theoretical Probability
2. Experimental Probability
3.   Axiomatic Probability

  Theoretical Probability:

It is based on the possible chances of something happening. The rationale behind probability is the foundation of theoretical probability. If a coin is tossed, for example, the theoretical probability of receiving a head is 12 percent.

Experimental Probability:

It is based on the results of a scientific study. Multiplying the total number of trials by the number of possible outcomes yields Experimental Probability. The experimental probability of heads is 6/10 or 3/5 if a coin is tossed 10 times and heads are recorded 6 times.

Axiomatic Probability:

A set of principles or axioms are established in the axiomatic probability that applies to all types. Kolmogorov established these axioms, which are known as Kolmogorov’s three axioms. The axiomatic approach to probability can be used to calculate the chances of events occurring or not occurring. The axiomatic probability lesson delves into this topic in-depth, including Kolmogorov’s three rules (axioms) and several other topics.

Application of probability:

Risk assessment and modeling are examples of how probability theory is used in everyday life..

Conclusion: 

The insurance industry and markets employ actuarial science to determine prices and make trading decisions. Probability is used in Environmental control, entitlement analysis, and financial regulation are all things that need to be considered. In a range of businesses and verticals, statistics is crucial for decision-making. It is utilized in marketing, e-commerce, banking, finance, human resources, production, and information technology. Furthermore, this mathematical discipline has played a vital role in research and is widely used in a variety of industries, including data mining, medicine, aerospace, robotics, psychology, and machine learning.