## What is Statistics

The term **statistics** is marked to have evolved from the Latin word *'status,'* or the Italian word *'Statista,'* or the German word *'Statistik,'* or the French word *'Statistique.'* Each of these words means *'Political State,'* and one of them is the root of the word 'Statistics.' Thus, as the name implies, the old-fashioned nature of statistics was known as the **'Science of Statecraft'** or the **'Science of Kings'** back then. The scope of statistics was limited to collecting data for state administration, i.e., army and public finance. However, statistics are now used in all fields of knowledge, including economics, business, management, natural science, political science, sociology, medicine, engineering, etc. Hence, statistics are used almost everywhere these days.

### Meaning and Definition of statistics in singular sense:

Statistics is that branch of mathematics which is concerned with data collection, analysis, interpretation, presentation, and organization. It is a method of describing, summarizing, and drawing conclusions about a population or a sample drawn from a population using numerical and graphical techniques.

In the singular sense, statistics refers to data collection, analysis, interpretation, presentation, and organization. It uses numerical and graphical techniques to describe, summarize, and make inferences about a population or a sample drawn from a population. Statistics is a branch of mathematics that uses statistical models and methods to analyze data and make informed decisions, predictions, or inferences about the population being studied. Statistical analysis requires a systematic and careful approach to ensure that the results are accurate and reliable.

Statistical analysis collects and analyses data to answer questions about a specific population or test hypotheses about relationships between variables. Statistical analysis uses the data to make informed decisions, predictions, or inferences about the population.

Many different types of statistical analysis can be performed, including descriptive statistics (which summarizes and describe the data), inferential statistics (which uses sample data to make inferences about a population), and predictive modelling (which uses statistical models to make predictions about future events). Statistics aims to use data to understand and make informed decisions about the world around us.

There have been many famous mathematicians who have contributed to the development of statistics and the study of data analysis. Here are a few examples of their definitions of statistics:

**John Tukey:** *"Statistics is the science of data."*

**George Box:** *"Statistics is the science of learning from data, and of measuring, controlling, and communicating uncertainty."*

**Ronald Fisher:** *"Statistics is the branch of scientific method which deals with the data obtained by counting or measuring the properties of natural phenomena."*

**David Cox:** *"Statistics is the branch of mathematics concerned with the collection, analysis and interpretation of data."*

**Frank Yates:** *"Statistics is the branch of applied mathematics concerned with the collection, analysis and interpretation of data."*

Overall, these definitions highlight the key aspects of statistics as a branch of mathematics that involves the collection, analysis, interpretation, and presentation of data in order to extract useful insights and make informed decisions.

**The four main features of statistics in the singular sense are:**

**Data collection:**Statistics involves collecting data from a population or a sample. This data can be collected through various methods, such as surveys, experiments, or observations.**Data analysis:**After the data has been collected, it must be analyzed to extract useful information and insights. This involves using statistical techniques and methods to summarize, describe, and make inferences about the data.**Data interpretation:**The results of the statistical analysis must be interpreted to understand their meaning and significance. This includes making conclusions about the relationships between variables and testing hypotheses about the population.**Data presentation:**Statistical analysis results should be presented clearly and concisely, using appropriate graphical and numerical techniques. This allows the results to be easily understood and communicated to others.

## Meaning and Definition of statistics in Plural sense:

In the plural sense, statistics refers to the individual pieces of data or numerical information collected, analyzed, and interpreted in statistical analysis. Statistics can be collected from a variety of sources. It can represent different data types, such as quantitative data (numerical values that can be measured or counted) or qualitative data (non-numerical information, such as words or categories).

The process of collecting and analyzing statistics typically involves the following steps:

**Defining the research question or hypothesis:**Before collecting data, it is essential to have a straightforward research question or hypothesis that the data will be used to answer or test. This helps to ensure that the data collected is relevant and appropriate for the study.**Selecting a sample:**In statistical analysis, collecting data from the entire population of interest is often impractical or impossible. Instead, a sample is selected from the population, and the data is collected from this sample. It is crucial to ensure that the sample is representative of the population to represent it accurately.**Collecting the data:**Many different methods can be used to collect statistical data, such as surveys, experiments, observations, or existing data sources. It is essential to ensure that the data is collected accurately and reliably.**Analyzing the data:**After the data has been collected, it must be analyzed to extract valuable insights and information. This may involve using statistical techniques to summarize and describe the data and testing hypotheses about relationships between variables.**Interpreting the results:**The statistical analysis's results must be interpreted to understand their meaning and significance. This includes making conclusions about the relationships between variables and testing hypotheses about the population.**Presenting the results:**The statistical analysis results should be presented clearly and concisely, using appropriate graphical and numerical techniques. This allows the results to be easily understood and communicated to others.

Overall, collecting and analyzing statistics involves using statistical methods and techniques to extract valuable insights and make informed decisions about a population or a sample drawn from a population. The individual pieces of data or numerical information collected and analyzed are called "statistics" in the plural sense.

Some of the definitions of statistics in the plural sense by famous mathematicians are listed as follows:

**John Tukey:** *"Statistics are the collection of data and their properties."*

**George Box:** *"Statistics are the individual pieces of data or numerical information that are collected, analyzed, and interpreted in statistical analysis."*

**Ronald Fisher:** *"Statistics are the individual pieces of data or numerical information that are collected and analyzed in statistical analysis."*

**David Cox:*** "Statistics are the individual pieces of data or numerical information that are collected and analyzed in statistical analysis."*

**Frank Yates:** *"Statistics are the individual pieces of data or numerical information that are collected and analyzed in statistical analysis."*

Overall, these definitions highlight the fact that statistics in the plural sense refer to the individual pieces of data or numerical information that are collected and analyzed in statistical analysis. These statistics are used to extract useful insights and make informed decisions about a population or a sample drawn from a population.

**The six main features of statistics in the plural sense are explained as under:**

**Data collection:**Statistics involves the collection of data from a population or a sample. This data can be collected through various methods, such as surveys, experiments, or observations.**Data type:**Statistics can represent different types of data, such as quantitative data (numerical values that can be measured or counted) or qualitative data (non-numerical information, such as words or categories).**Sample selection:**In statistical analysis, it is often impractical or impossible to collect data from the entire population of interest. Instead, a sample is selected from the population and the data is collected from this sample. It is important to ensure that the sample is representative of the population in order to accurately represent the population.**Data analysis:**After the data has been collected, it must be analyzed in order to extract useful insights and information. This may involve using statistical techniques to summarize and describe the data, as well as testing hypotheses about relationships between variables.**Data interpretation:**The results of the statistical analysis must be interpreted in order to understand their meaning and significance. This includes making conclusions about the relationships between variables and testing hypotheses about the population.**Data presentation:**The results of the statistical analysis should be presented in a clear and concise manner, using appropriate graphical and numerical techniques. This allows the results to be easily understood and communicated to others.

Overall, these six features of statistics in the plural sense are essential for using individual pieces of data or numerical information to extract useful insights and make informed decisions about a population or a sample drawn from a population.

### Functions/ Needs and Importance of Statistics

Statistics were once used to formulate fiscal and military policies. As a result, it was known as the "Science of King." However, statistics are widely used in modern times. It is applied in various fields, including economics, planning, business and management, pure science, social science, etc. The following sections discuss the scope and importance of statistics in various sectors and disciplines:

**Statistics in economics:**Statistical data and techniques are extremely useful in studying and solving various economic problems such as consumption, production, distribution, exchange, wages, prices, saving, investment, employment, poverty, etc. Statistics can also be used to develop economic theories and policies. Similarly, it aids in forecasting economic variables such as demand, supply, production, cost, national income, population, etc. Furthermore, it aids in comparing economic data and presents it using various tools such as pie charts, line graphs, bar diagrams, tables, etc. Thus, in the modern era, economics and statistics are complementary.**Statistics in business and management:**Statistics have numerous applications in business and management. In the modern era, business activities have become increasingly multidimensional and they are becoming increasingly complex. Statistics can be used to reduce the complexity of business and management fields, which reduces the complexities of business and management problems. As a result, statistics aid in analyzing and resolving problems such as production control, determining the quality and quantity of raw materials and labor, and determining the commodity's quantity, shape, size, and color.**Statistics in planning:**The modern era is known as the age of planning. Work can only be successful if it is well-planned. As a result, organizations, individuals, and the government of a country develop plans for efficient work, efficient allocation of scarce resources, and the formulation of policy decisions. The success of the planning is dependent on the accurate and thorough analysis of the statistical data.- Â
**Statistics to the state:**A state needs statistics because they help with administration and policy creation. A state must evaluate the advantages and disadvantages of any policy before enforcing it, and this can only be done with the aid of numerical facts. For instance, the government implements numerous policies that all rely on statistics, including fiscal and monetary policy, employment policy, poverty alleviation policy, and so forth. **Statistics in natural (Pure) science:**The study of natural /pure sciences such as physics, chemistry, biology, astronomy, and others benefits from using statistics. Additionally, it is helpful in fields of science like engineering, medicine, environmental science, etc. All of the natural sciences and science-related subjects extensively use information or numerical facts, facilitating learning and the development of new theories.**Statistics in social sciences:**The social science-related fields of sociology, history, political science, psychology, anthropology, criminology, etc., benefit greatly from statistics. These courses all examine society and human behavior. Numerous statistical tools, including mean, mode, median, dispersion, regression, correlation, etc., are used to study and analyze social and human behavior. Demography is another crucial area of social science that heavily relies on applying statistics. The study becomes difficult and incomplete without using statistical tools in these areas.**Statistics in mathematics:**Mathematics and statistics are related. Today, statistics is also thought of as the area of applied mathematics that focuses on examining numerical facts or data, Similar to how statistics are necessary for creating various mathematical models in mathematics. Therefore, a new branch of mathematical statistics has emerged due to the growing importance of mathematics in statistical analysis.

### Uses and Importance of Statistics in Economics:

Statistics plays a vital role in economics, as it is used to collect, analyze, and interpret data in order to understand and make informed decisions about economic phenomena and trends. Some specific ways in which statistics is used in economics include:

**Measuring economic indicators:**Statistics is used to collect and analyze data on economic indicators such as GDP, unemployment rate, inflation rate, and consumer spending, among others. These indicators provide important information about the overall state of an economy and can be used to forecast future economic trends.**Evaluating economic policies:**Statistics is used to collect and analyze data on the effects of different economic policies, such as tax cuts, spending increases, or regulatory changes. This helps policymakers to evaluate the effectiveness of these policies and to make informed decisions about their implementation.**Analyzing market trends:**Statistics is used to collect and analyze data on market trends, such as changes in consumer demand, supply, and prices. This helps businesses and investors to make informed decisions about buying and selling goods and services.**Modelling economic phenomena:**Statistics is used to develop statistical models that can be used to understand and predict economic phenomena, such as consumer behaviour, market trends, or the effects of economic policies. These models can be used to make informed decisions about economic issues and to forecast future economic trends.

Overall, the use of statistics in economics is essential for understanding and making informed decisions about economic phenomena and trends. It allows policymakers, businesses, and investors to analyze and understand economic data in order to make informed decisions and predictions about the future.

### Uses of Statistics in the Stock Market:

Statistics plays a vital role in the stock market, as it collects, analyses, and interprets data to understand and make informed decisions about financial investments. Here are eleven specific ways in which statistics are used in the stock market:

**Analyzing market trends:**Statistics is used to collect and analyze data on market trends, such as changes in stock prices, trading volume, and market indices. This helps investors to make informed decisions about buying and selling stocks.**Evaluating company performance:**Statistics is used to collect and analyze data on a company's financial performance, such as revenue, profits, and financial ratios. This helps investors evaluate a company's health and potential growth and make informed decisions about buying or selling its stock.**Forecasting future stock prices:**Statistics is used to develop statistical models that can be used to predict future stock prices based on historical data and other factors. Investors can use these models to make informed decisions about buying or selling stocks.**Analyzing risk and return:**Statistics is used to analyze data on the risk and return associated with different stocks and portfolios. This helps investors to understand the trade-offs between risk and return and to make informed decisions about their investments.**Evaluating portfolio performance:**Statistics is used to collect and analyze data on the performance of an investor's portfolio, including returns, risk, and diversification. This helps investors evaluate their investment strategies' effectiveness and make informed decisions about their portfolios.**Analyzing market efficiency:**Statistics is used to collect and analyze data on the efficiency of financial markets, including the speed at which information is incorporated into stock prices and the level of liquidity in the market.**Analyzing investor behaviour:**Statistics is used to collect and analyze investor behaviour data, including factors influencing investment decisions and market trends.**Evaluating the performance of mutual funds:**Statistics is used to collect and analyze data on the performance of mutual funds, including returns, risk, and fees. This helps investors to evaluate the effectiveness of different mutual funds and to make informed decisions about their investments.**Evaluating the performance of hedge funds:**Statistics is used to collect and analyze data on the performance of hedge funds, including returns, risk, and fees. This helps investors to evaluate the effectiveness of different hedge funds and to make informed decisions about their investments.**Evaluating the performance of exchange-traded funds (ETFs):**Statistics is used to collect and analyze data on the performance of ETFs, including returns, risk, and fees. This helps investors to evaluate the effectiveness of different ETFs and to make informed decisions about their investments.**Modelling stock prices:**Statistics is used to develop statistical models that can be used to understand and predict stock price movements. These models can make informed decisions about buying or selling stocks and forecast future price trends.

Overall, using statistics in the stock market is essential for understanding and making informed decisions about financial investments. It allows investors to analyze and understand financial data to make informed decisions and predictions about the performance of different stocks and portfolios.

### Limitation of statistics

Statistics has numerous applications in almost every aspect of human life. Statistics are almost universally applicable. Statistics, despite its many applications, has some limitations, which are as follows:

**Statistics do not study individuals:**Statistics is concerned with aggregate objects and does not provide specific reform to individual items in a series. Individual items, such as a girl's beauty or a person's height, do not constitute statistical data and are, therefore, meaningless in a statistical investigation. Individual agricultural production figures are meaningless. As a result, statistical analysis is only appropriate for problems involving group characteristics.**Statistics is not suitable for studying a qualitative phenomenon:**Statistics studies quantitative characteristics of given problems rather than qualitative characteristics. Statistics do not directly study problems related to qualitative phenomena, such as honesty, poverty, leadership, intelligence, and so on.**Statistical laws are not exact:**Statistical laws, unlike physical and natural science laws, are only approximations and not exact. In statistics, there are only a few completely correct results, and almost all are only roughly correct. In other words, statistical laws are only true on average.**Statistics is liable to be misused:**The most significant limitation of statistics is that experts must use them. When inexperienced people use statistical methods, statistical tools provide incorrect information and must draw incorrect conclusions. As a result, statistics can be dangerous in the hands of an inexperienced person.**Statistics is only a means:**Statistics only provides a method for studying a problem. There are additional methods. These methods should be used to supplement the conclusions reached through statistical analysis.

### Conclusion:

The term "statistics" appears to be derived from the Latin word "status." Back then, it was known as the "science of statecraft." Statistics are now used in economics, business and management, natural science, sociology, medicine, and engineering. The modern era is known as the planning era. Work can only be considered successful if it is meticulously planned. The accuracy and thoroughness of the statistical data analysis are critical to the success of the planning. Statistics are also useful in scientific fields such as engineering, medicine, and environmental science.

Statistics is now considered a branch of applied mathematics that focuses on analyzing numerical facts or data. As a result of the growing importance of mathematics in statistical analysis, a new branch of statistics known as mathematical statistics has emerged. Statistics' most significant limitation is that experts must use them.

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