Statistics is a branch of applied mathematics that involves the collection, description, analysis, and inference of conclusions from quantitative data. The mathematical theories underpinning statistics are largely based on differential and integral calculus, linear algebra, and probability theory.

## Understanding Statistics

Statistics is used in virtually all scientific disciplines, such as the physical and social sciences, as well as in business, the humanities, government, and industry. Statistics is fundamentally a branch of applied mathematics that developed from the application of mathematical tools such as calculus and linear algebra to probability theory.

In practice, statistics is the idea that we can learn about the properties of large sets of objects or events (a population) by studying the characteristics of a smaller number of similar objects or events (a sample). Since collecting comprehensive data on an entire population is in many cases too expensive, difficult, or outright impossible, statistics begins with a sample that can be conveniently or affordably observed.

## Who uses Statistics?

Statistics is widely used in a whole range of applications and professions. Every time data is collected and analyzed, statistics are made. Consequently, this can range from government agencies to academic research or investment analysis.

## Theoretical Statistics

Theoretical statistics is concerned with general classes of problems and the development of a general methodology. Statisticians often develop models based on probability theory. Probability theory is the branch of mathematics that develops models for “chance variations” or “random phenomena.” It originated as a discipline when mathematicians in the 17th century began to calculate the probabilities in various games of chance.

They soon saw how to make applications of the theory they developed to the study of errors in experimental measurements and to the study of human mortality (for example, by life insurance companies). Today, probability theory is an important field with wide applications in science and engineering. Some examples are:

Modeling of the appearance of sunspots to improve radio communication,

Modeling and control of congestion on highways and

Reliability theory to assess the probability that a space vehicle will function throughout a mission.

## Statistical Problems

Statisticians, people who study statistics, are especially concerned with determining how to draw reliable conclusions about large groups and general events from the behavior and other observable characteristics of small samples. These small samples represent a part of the large group or a limited number of cases of a general phenomenon. To do this, it is often necessary to use computer data analysis techniques. Some examples of statistical problems are:

Interpretation of evidence linking environmental factors and disease

Design of experiments to evaluate the efficacy of pharmaceutical products

Data mining to discover target segments in the population

Market study to estimate the demand for a new product

Opinion polls in politics

Estimating the size of an animal population to help set conservation standards

Reliability studies to determine guarantees

Improving the quality of a service or manufactured item

Weather forecast

Error analysis in scientific experiments and

Stock Price Prediction

## Professionals in the area of Statistics

Statisticians are key contributors to scientific methodologies. They use their quantitative knowledge to design data collection plans, process them, analyze them and interpret the results. Furthermore, statisticians often make critical assessments of the reliability of the data and whether the inferences drawn from it can be made with confidence. They also help identify misleading abuses of data that may be portraying an inaccurate account of a situation.

The characteristics of the work of people in the statistical professions include the following activities:

Use data to solve problems in a wide variety of fields

Apply mathematical and statistical knowledge to social, economic, medical, political, and ecological problems

Work individually and/or as part of an interdisciplinary team

Travel to consult other professionals or attend conferences, seminars and continuing education activities and

Advancing the frontiers of statistics and probability through education and research

## Main Areas

The two main areas of statistics are known as descriptive statistics, which describes the properties of sample and population data, and inferential statistics, which uses those properties to test hypotheses and draw conclusions.

Two types of statistical methods are used to analyze the data: descriptive statistics and inferential statistics. Statisticians measure and collect data about the individuals or items in a sample, and then analyze this data to generate descriptive statistics. They can then use these observed characteristics of the sample data, properly called “statistics,” to make inferences or guesses about unmeasured (or unmeasurable) characteristics of the larger population, known as parameters.

#### Descriptive statistics

Descriptive statistics focuses primarily on the central tendency, variability, and distribution of the sample data. Central tendency is the estimate of characteristics, a typical element of a sample or population, and includes descriptive statistics such as the mean, median, and mode. Variability refers to a set of statistics that show how much difference there is between items in a sample or population across measured characteristics, and includes metrics such as range, variance, and standard deviation.

Distribution refers to the general “shape” of the data, which can be represented on a graph as a histogram or dot plot, and includes properties such as the probability distribution function, skewness, and kurtosis. Descriptive statistics can also describe the differences between the observed characteristics of items in a data set. Descriptive statistics help us understand the collective properties of the elements in a data sample and form the basis for testing hypotheses and making predictions using inferential statistics.

#### inferential statistics

Inferential statistics refers to the tools that statisticians use to draw conclusions about the characteristics of a population, drawn from the characteristics of a sample, and to decide how confident they can be of the reliability of those conclusions. Based on the size and distribution of the sample, statisticians can calculate the probability that statistics, which measure central tendency, variability, distribution, and relationships among features within a data sample, give an accurate picture. of the corresponding parameters of the entire population from which the sample is drawn.

Inferential statistics are used to make generalizations about large groups, such as estimating the average demand for a product through a survey of consumer buying habits, or to attempt to predict future events, such as projecting the future profitability of a product. value or asset class based on the returns of a sample period.

## What is the difference between descriptive and inferential statistics?

Descriptive statistics is used to describe or summarize the characteristics of a sample or data set, such as the mean, standard deviation, or frequency of a variable. Inferential statistics, by contrast, employs any number of techniques to relate variables in a data set to each other, for example using correlation or regression analysis. In this way, forecasts can be estimated or causality inferred.

The output of a regression model is often analyzed for statistical significance, which refers to the statement that a finding result generated by testing or experimentation is not likely to have occurred by chance or chance, but is likely to be attributable to a specific cause elucidated by the data.

Having statistical significance is important for academic disciplines or professionals that rely heavily on data analysis and research.

## What are the Statistical Tools?

Some common statistical tools and procedures are as follows:

Mean (average)

variance

Asymmetry

kurtosis

inferential

Linear regression analysis

Analysis of variance (ANOVA)

Logit/Probit Models

Null hypothesis tests