Statistics refers to the branch of study which consists of gathering and organizing as well as analyzing and interpreting and presenting data. Its customary to start with a statistical population or model to be researched while applying the statistics to a scientific or industrial or social problem. The statistical population consists of a wide range of people and objects including all the individuals living in a country or every atom in a crystal. Statistics is concerned with all the aspects of data such as data collection planning in the form of experiments and surveys.

Statisticians construct specific experiment designs and sample surveys to acquire data when the census data is unavailable. This type of representative sampling also ensures that the inferences drawn and conclusions arrived at can be extrapolated to the entire population. On the other hand, experimental study comprises of measuring the system under investigation and altering it. And also measuring the new values by making use of the same process to see if the alteration has changed the measurements’ values. The observational study, on the other hand, does not entail any such experimental modification.

Data analysis primarily consists of two statistical methods. Descriptive statistics is the first method which uses indices like the mean deviation and standard deviation. This method is used for summarizing the sample data. And the second method is inferential statistics that derives conclusions and inferences from data. However, this data unlike in descriptive method is subject to random variation i.e., observational errors and sampling variation. Moreover, descriptive statistics is the method thats often deals with two distributional properties of sample or population.

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The central tendency or location property characterizes the central or typical value of the distribution. Whereas dispersion or variability property seeks to characterize the extent of deviation of the values of distribution from its central values and from each other.

Probability theory dealing with examination of random processes, is used to draw conclusions using mathematical statistics. The standard technique of statistics involves gathering data in order to assess the link between two sets of statistical data. And also between a data set and a synthetic data produced using an idealized model. The statistical link between the two sets of data is hypothesized, and its contrasted to an idealized null hypothesis of no relation between the data sets.

Statistical tests are used for showing that the null hypothesis can be shown wrong, given the evidence presented in the test are used to reject or disprove the null hypothesis. When working with a null hypothesis, there are two types of errors to be aware of: Type I errors (where the null hypothesis is incorrectly rejected, resulting in a “false positive”) and Type II errors (null hypothesis is not rejected and the actual relation between the population is missed giving a “false negative”). Several issues have been linked to the framework, including getting a sufficient sample size and defining an adequate null hypothesis.

Errors can also be found in the techniques of measurement that create the statistical data. Most of the errors are characterized as random (noise) and systematic (bias), although other sorts of errors (for example, blunder, when an analyst reports erroneous units) can also occur. Missing data and censoring can cause estimates to be skewed, and particular strategies have been developed to overcome these issues.

## What is Statistics?

Statistics is a discipline of mathematics that deals with the collection and analysis as well as interpretation and explanation or presentation of data. Statistics is sometimes considered a separate branch of mathematical science rather than a subject of mathematics. While data is used in many scientific projects, statistics is also concerned with using data in the situations of uncertainty and making decisions in situations of uncertainty.

The application of statistics to a problem begins with the identification and study of a population or process thats to be studied. Population in this context refers to anything from ‘all the individuals residing in a country’ to ‘every atom constituting a crystal’. Generally, statistician collect data on the whole population and this operation is called the census. Governmental statistical institutes are usually in charge of this. To summarize population data descriptive statistics may also be employed. For the data of continuous nature (such as income), numerical descriptors such as mean and standard deviation are useful. However, frequency and percentage are better suited for data of categorical nature (such as education).

If its not possible to conduct a census, a sample of the population is examined and studied. Data is therefore collected in the form of samples in an observational setting or experimental environment. Moreover, its done only after a representative sample has been identified from of the entire population. For summarizing the sample data, descriptive statistics might be employed. However, because the sample is drawn at random, the numerical descriptors derived from it are likewise subject to ambiguity. Inferential statistics are required to generate significant inferences regarding the whole population.

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It makes judgments regarding the population represented by the sample data by relying on the patterns found in the sample. The conclusions drawn maybe in the form of yes or no questions regarding the data (hypothesis testing) or predicting its numerical properties (estimation). Characterizing data associations (correlation) and modelling relationships within the data (for example, using regression analysis) are all examples of inferences. Forecasting and predicting as well as the estimating the unknown values either in or connected with the population being investigated are all examples of inference. Extrapolation and interpolation of time series and spatial data as well as data mining are also such examples.

## History of Statistics

Statistical inferences and writings were first written by cryptographers and Arab mathematicians.  Its during the period between eighth and thirteenth centuries, also known as the Islamic Golden Age period. The Book of Cryptographic Messages, written by Al-Khalil (717–786), used the permutations and combinations for the first time. They were used for enumerating all conceivable Arabic words with and without vowels. Al-Kindi revealed the manner of utilizing frequency analysis for decrypting encrypted signals, in his book titled Manuscript on Deciphering Cryptographic Messages. Al-Kindi is also credited with developing the first statistical methods used for decrypting encrypted messages. However, its later refined by him by him and later Arab cryptographers.

Later, Ibn Adlan (1187–1268) made a significant addition to frequency analysis by using sample size. Natural and Political Observations concerning the Bills of Mortality, published by John Graunt in 1663, is the earliest European work on statistics. The requirement for states to develop policies on the basis of demographic and economic data led to the earlier developments in statistical thought. In the beginning of the nineteenth century, the scope of statistics discipline expanded to cover the collection and analysis of data in general. Statistics is now widely used in government sector and industries as well as in the social sciences.

Along with the introduction of probability theory by Gerolamo Cardano and Blaise Pascal along with Pierre de Fermat in the seventeenth century, the mathematical underpinnings of contemporary statistics were created. The probability concept was already addressed in mediaeval law and by the philosophers like Juan Caramuel. However, the probability theory of mathematics developed from the study of games of chance. Adrien-Marie Legendre was the first to describe the least squares approach in the year of 1805.

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The field of statistics in its present form developed during the later half of the 19th and earlier parts of the 20th centuries. The efforts of Francis Galton and Karl Pearson lead to the evolution of statistics into a discipline of mathematics. Thereafter, statistics was being utilized for analyzing data not only in science, but also in industry and politics. This furthermore led the first wave around the turn of the century. Contributions of Galton consist of developing the standard deviation concepts and correlation and regression analysis.  It also comprises of application of the aforementioned in the study of a number of human traits, including height and weight etc.

Pearson invented numerous items, including the Pearson product-moment correlation coefficient thats defined to be a product moment. He also invented the method of moments for fitting distributions to samples and the Pearson distribution method. The first publication of mathematical statistics and biostatistics (then known as biometry) called Biometrika was the contribution of Galton and Pearson. Pearson also established the first university statistics department in the world at University College in London.

William Sealy Gosset started the subsequent wave in the years of 1910 and 1920 which culminated in Ronald Fisher’s insights. He also published the textbooks that defined the academic discipline in universities all over the world. His seminal 1918 paper The Correlation between Relatives on the Supposition of Mendelian Inheritance (which used the statistical term variance for the first time) was a significant publication. Furthermore, his classic work in 1925 on Statistical Methods for Research Workers, and The Design of Experiments published in 1935 were among his most important contributions.

##### Sufficiency and supplementary statistics-

Sufficiency and supplementary statistics as well as Fisher’s linear discriminator and information are all notions he invented. Fisher’s principle (called “probably the most celebrated argument in evolutionary biology” by A. W. F. Edwards). And a concept in sexual selection regarding positive feedback runaway affect seen in evolution called Fisherian runaway were among the biological concepts he applied statistics. The final wave mainly comprising of refinement and expansion of prior advances arose from Egon Pearson and Jerzy Neyman’s combined work in the 1930s.

They covered the terms “Type II” error and test power as well as confidence intervals. In the year of 1934, Jerzy Neyman demonstrated that sampling randomly was a better method of estimation than purposive (quota) sampling method. Statistical approaches are now used in all sectors that need decision-making. Its also used for producing reliable inferences from a large body of data and for decision making using statistical methodology in situations of ambiguity. Modern computers have increased the speed of statistical computations of large scale and enabled introduction of novel procedures that would be impossible to accomplish manually.

## Types of Statistics

Statistics is a way of interpreting and analyzing as well as summarizing data in mathematics. As a result, on the basis of the characteristics types of statistics can be described as descriptive and inferential. We analyze and evaluate data based on how its represented. Its done using pie charts and bar graphs and tables. Statistics is a branch of mathematics thats once thought to be the science of many sorts of statistics. For instance, the gathering and analysis of information regarding a country’s economy and population. And also about its military and literacy and so on. The statistics encompass linear algebra and stochastic analysis as well as differential equations and measure-theoretic theory of probability.

Statistical analysis, in its most basic form, is used to collect and analyze huge amounts of data. Statistics is a discipline of mathematics in which large amounts of data are computed using charts and tables and graphs. Here, the data acquired for analysis is referred to as measurements. Now, if we need to measure data depending on a scenario, we take a sample from the population. The analysis or computation for the next measurement is then carried out.

### Descriptive Statistics

The data summary is prepared using the specified observations already provided, in this sort of statistics. The summary is a representation of a population thats drawn from a sample population. Furthermore, its done using the mean and standard deviation parameters. Descriptive statistics is a means to use tables and graphs, as well as summary measures for organize and portraying and describing a set of data. For instance, data regarding a group of people in a city who use the internet or watch television can be collected through this method. Descriptive statistics are further divided into four categories:

• Frequency measurement
• Dispersion measurement
• Central tendency measurement.
• Positional measurement

The measurement of frequency shows how many times a given piece of data appears. Dispersion is measured by calculating range and variance as well as standard deviation. It determines the extent to which data is disseminated. The data’s mean and median along with mode represent its central tendencies. The percentile and quartile ranks are described by the position measurements.

### Inferential Statistics

The meaning of descriptive statistics is interpreted using inferential statistics. That is, we utilize these statistics to understand significance of the data obtained after collecting and analyzing and summarizing it. Or, to put it another way, its used to derive inferences from those data which are subject to random changes like observational mistakes and sample variance etc. Inferential statistics is a strategy that permits us to make judgements and predictions or draw inferences from a population using sample data. It allows us to make statements that go beyond what is available in terms of data or information. Estimations using hypothetical study and research are examples of inferential statistics.

## Scope of Statistics in India

The study of data gathering and organizing along with analysis and interpretation and presentation is known as statistics. Probability is a branch of mathematics thats used to construct it. We can use probability to figure out the likelihood of an event. It also provides a means for discussing this unpredictability. Its applicable to a wide range of scientific fields, including psychology and economics, medicine and advertising and demography etc. Students can learn the fundamentals of logic and mathematics as well as statistical reasoning. They can also study data analysis and data evaluation and research procedures by pursuing statistics course.

Statistics plays a critical role in our modern era, which has been dubbed the age of planning. Most governments across the globe are continuously looking for ways to boost their economic development. The economic issues of wages and prices and time series analysis and demand analysis can be solved with statistical data and statistical analysis tools. Its an indispensable production control tool. For understanding client preferences, businessmen are increasingly depending on statistical approaches.

Statistics from the industry are frequently used to monitor equality. Statistical techniques of inspection planning and control chart are commonly used in production engineering to determine whether or not the product conforms to the standards. Bankers and insurance companies as well as social workers can make use of statistics. Additionally, labor unions and trade groups and chambers, and politicians all benefit from statistics.

## Eligibility Criteria for Statistics in India

If a student wants to pursue an undergraduate course in statistics, he must meet all of the entry requirements set forth by universities. In order to get into the best colleges offering undergraduate degrees, the student must meet the following eligibility criteria:

• The candidate should have successfully completed 10 + 2 education from a recognized board.
• Mathematics must be one of the key topics studied by the students in class 12 for applications to be considered.
• A strong performance in English language proficiency exams such as the IELTS, TOEFL, and others are required for admissions in international institutions. A minimum SAT or ACT score is necessary.
• Those who want to pursue this study in India however require candidates to pass admission tests such as the GSAT and BHU UET and DSAT and SUAT among others.

A B. Sc. degree in statistics/mathematics or a degree of equivalent value in statistics with computer applications is required to undergo M. Sc. in Statistics. Several colleges have a cutoff percentage for students to be considered for admission. The cut off maybe overall or limited to a particular section. For example, some institutions may have a minimum per cent in mathematics as a cutoff regardless of the cumulative marks.

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Aside from that, some universities also require the candidate to qualify the entrance exam. Academic records and written exam scores and marks of the personal interviews are also used to select students. The written exam generally consists of two types of questions: Objective and Descriptive type questions.

Basic statistics and probability theory and computer principles are all covered in the curriculum. Candidates must have basic numerical skills as well as the capacity to work comfortably with numbers. They should also analyze the trends and patterns along with using statistics to collect information from sophisticated data. Moreover, they need to interpret the results to identify the causes of the problems and recommend solutions to these problems.

## Statistics Entrance Exams

Statistics is the science that deals with the collection and organization as well as analysis of the data. An undergraduate degree in the relevant discipline is the minimum requirement for admission to the postgraduate courses. Statistics courses are available at several universities. They will, however, need to sit for an entrance exam if they choose to pursue advanced education. Some of statistics exams in India are:

Agra University Entrance Exam, Aligarh Muslim University: Department of Statistics and Operations Research Entrance Exam, Amrita University Entrance Exam, Andhra University Entrance Exam, Annamalai University Entrance Exam, Banaras Hindu University Entrance Exam, Banasthali Vidyapith Entrance Exam, Bangalore University Entrance Exam, Barkatullah University Entrance Exam, Bharathiar University Entrance Exam.

Bhartiya Vidyapeeth Entrance Exam, Devi Ahilya Vishwavidyalaya: School of Statistics Entrance Exam, Dr. BR Ambedkar Marathwada University Entrance Exam, Gandhigram Rural Institute University Entrance Exam, Gauhati University Entrance Exam

Himachal Pradesh University Entrance Exam, Indian Institute of Technology – Joint Entrance Exam (IIT EE), Indian Statistical Institute Entrance Exam, Kalinga Institute of Industrial Technology Entrance Examination (KIITEE).

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Karunya University Entrance Exam, Kurukshetra University Entrance Exam, Madurai Kamraj University Entrance Exam, Maharaja Ganga Singh University Entrance Exam,  Maharishi Dayanand University Entrance Exam, Mahatma Gandhi University Entrance Exam, Mohanlal Sukhadia University Entrance Exam

Narsee Monjee Institute of Management and Higher Studies (NMIMS) Entrance Exam, North Eastern Hill University (NEHU) Entrance Exam, North Gujarat University Entrance Exam, Osmania University Entrance Exam, Pondicherry University Entrance Exam

Punjab University Entrance Exam, Punjabi University Entrance Exam, Sambalpur University Entrance Exam, Sardar Patel University Entrance Exam, Saurashtra University Entrance Exam, Serampore University Entrance Exam, Shivaji University Entrance Exam, South Gujarat University Entrance Exam

University of Allahabad Entrance Exam, University of Calcutta Entrance Exam, University of Calicut Entrance Exam, University of Delhi Entrance Exam, University of Hyderabad PhD Statistics Entrance Exam

University of Kerala Entrance Exam Entrance Exam, University of Madras Entrance Exam, University of Mysore Entrance Exam, University of Pune Entrance Exam, University of Rajasthan Entrance Exam, Vinayaka Missions University Entrance Exam

## Top Statistics Courses in India

Statistics – a discipline of mathematics thats commonly utilized for data analysis and research. Statistics can be studied at all levels of education, including certificate courses and diplomas. They are also available in the form of post-graduate diplomas and undergraduate, postgraduate and doctoral degree courses. Furthermore, certificate and diploma programs are common ways to learn the subject. These courses can taken either online or offline. This makes it possible to learn the courses while also being engaged in full-time work. Several of these certificate courses in statistics are free to enrol in. However, some demand a nominal price for a certificate of completion. Certificate programs can last anywhere from a few hours to six months. Diploma and postgraduate diploma courses can completed in one or two years. Undergraduate, postgraduate and doctoral degrees take three years, two years, and three years to accomplish, respectively.

## Top Statistics Courses for Bachelors in India

### B Sc.:

The Bachelor of Science in statistics (B. Sc. Statistics) is a three-year undergraduate program that covers topics such as probability and statistical methods. Similarly, survey sampling and numerical analysis are also included in this study. The course consists of lectures as well as flying and simulation training. Assignments and other activities targeted at providing both classroom and practical instruction are also part of this curriculum. Students interested in pursuing a B. Sc. in Statistics must have finished 10+2. They must have studied physics and Chemistry as well as mathematics subjects.

For B. Sc. Statistics admission, a minimum of a 50% grade from a recognized Indian school is required. Top colleges in India offering B. Sc. degree provide admissions on the basis of merit. They also consider the scores obtained in entrance tests like as GSAT and BHU UET, also IISER IAT among others. The typical annual fees for a B. Sc. Statistics degree range from Rs. 20, 000 to Rs. 1, 50, 000. In the next five years, this industry is predicted to generate more than 20 lakh jobs. The average cost of a course is between Rs. 20, 000 and Rs. 1, 50, 000. After completing this degree students get placed in the job roles of Risk analyst and Statistician as well as Actuary Manager. Also, Research professional and Credit Risk Strategist along with Analysis or Statistics Manager. And Subject Matter Expert.

### List of Top B. Sc. Colleges in India

 College Name Affiliated University Cut Off Ramnarain Ruia Autonomous College Lady Sriram College for Women DG Ruparel College of Arts Science and Commerce Shaheed Rajguru College of Applied Sciences for Women Indian Academy Group of Institutions AV College of Arts Science and Commerce Indian Institute of Management and Commerce

Average Fees for B. Sc.: Rs. 20, 000 to Rs. 1, 50, 000

Admission Criteria for B. Sc.: Entrance based as well as merit based

Types of Jobs after B. Sc.: Risk analyst and Statistician as well as Actuary Manager. Also, Research professional and Credit Risk Strategist along with Analysis or Statistics Manager. And Subject Matter Expert.

Average Placements after B. Sc.: Rs. 4, 50, 000- Rs. 8, 00, 000.

## Top Statistics Courses for Masters in India

### MSc.:

M Sc. Statistics (Master of Science in Statistics) is a postgraduate program available in statistics discipline. Its concerned with the study of how data is collected and organized, and interpreted. It deals with all areas including data collection planning in terms of survey and experiment designing. M. Sc. Statistics program typically lasts two academic years, but this differs according to the institute. The candidates intending to pursue this degree need to have obtained a B. Sc. degree in Mathematics or Statistics. They can also have a graduation from a recognized university in a relevant discipline. Its the eligibility criteria required for appearing for the entrance to this program.

A majority of M. Sc. Statistics students are admitted to the institutions through an entrance examination. A few colleges do, however, admit students based on their merit. In India, the average fee for an M. Sc. in Statistics is between Rs. 5,000 and Rs. 65,000. This course will teach you how to solve statistical challenges in the real world. Subjects including computational statistics and statistical machine learning as well as the fundamental principles of statistical inference are all part of the M. Sc. Statistics curriculum.

M Sc. Statistics graduates find work in consultancies, where they analyze people’s preferences and habits. Other fields of employment include marketing, finance, and data metrics. In India, the average annual pay for successful M. Sc. Statistics postgraduates ranges from Rs. 3,00,000 to Rs. 7,00,000. A candidate who successfully completes the MSc Statistics course can pursue further study and research in this discipline. They can pursue a doctorate in statistics and then work as college lecturers.

### List of Top M. Sc. Colleges in India

 College Name Affiliated University Cut Off/Merit Based Hindu College New Delhi Christ University Bangalore Ramjas College New Delhi Aligarh Muslim University The Oxford College of Science Bangalore Sri Venkateswara College Madras Christian College

Average Fees for M. Sc.: Rs. 5,000- Rs. 65,000

Admission Criteria for M. Sc.: Entrance based as well as merit based

Types of Jobs after M. Sc.: Statistician and Investment Analyst as well as Arithmetician. Also, Cost Estimator and Online Tutor and Service Estimator along with Subject Matter Expert. Also, Assistant Professor and Statistical Investigator.

Average Placements after M. Sc.: Rs. 3,00,000 to Rs. 7,00,000

## PhD. in Statistics

PhD Statistics is a two-year doctoral program in statistics that can be undertaken after the Master’s degree has been completed. This PhD course deals with the gathering, analysis and interpretation as well as presentation of numerical data thats a branch of mathematics. This program helps in the determination of variability of measuring systems and control procedures for bridging data. Along with the making of data-driven decisions. This course of study encompasses a wide range of academic subjects, from physical to humanities and social sciences discipline. Mathematical and Applied Statistics are both studied in the field of statistics. Candidates must have completed an M. Sc. or M. A. in mathematics or statistics with average grade point of at least 55 per cent to be considered for this program.

Admission to the PhD Statistics program will be based on the performance of the candidate in the postgraduate degree test. It can also be based on their success in the entrance exams administered by the institutions. PhD statistics graduates work as Research Analysts and Assistant Professors as well as Data Analysts. They also find jobs as Biostatisticians and Data Interpreters as well as Research Scholars among other positions. They find employment in the fields of Statistical Services and Social Research as well as Economics and Finance. Indian Economic Services and Businesses and Commerce, as well as Government Jobs Consulting Firms and other fields, also employ them.

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In India, the average annual tuition expense for this program ranges from Rs. 10, 000 to Rs. 1, 50, 000. A PhD Statistics degree holder’s average annual pay in India ranges between Rs. 3, 00, 000 and Rs. 8, 00, 000. Students can continue as independent researchers and get their research papers published if they choose to pursue more research. M Phil Mathematics and M Phil Statistics are also options available for these students. In the future, they may also pursue a D. Sc. (Doctor of Science) degree in the relevant field.

### Colleges/Universities offering PhD. in Statistics

 College Name Affiliated University Eligibility Banaras Hindu University University of Hyderabad Aligarh Muslim University Amity University Aligarh Muslim University Pondicherry University Banasthali Vidyapeeth

Average Fees for PhD. in Statistics: Rs. 10, 000 to Rs. 1, 50, 000.

Admission Criteria for PhD. in Statistics: Entrance based as well as merit-based

Average Placements after PhD. in Statistics: Rs. 3, 00, 000 and Rs. 8, 00, 000.

### What to do after PhD. in Statistics?

PhD in Statistics – an excellent analytic program thats research-based and suitable for those interested in expanding knowledge and expertise. This program enhances one’s skills in aspects of numerical data including collection and analysis and interpretation as well as presentation. Candidates’ research may result in furthering the field of statistics. Its achieved by introducing changes in documentation and legislation as well as instruction and technology. Its a field of study that encompasses a wide range of academic disciplines from the humanities to the physical and social sciences. Mathematical and Applied Statistics are both studied in the field of statistics. Furthermore, the study of applied statistics – divided into two categories: descriptive statistics and inferential statistics.

The pursuit of a PhD in statistics will determin by the aims and goals of each individual. The Statistics course prepares students for employment in academia and government as well as non-profit organizations. They also teach them to think critically and creatively as well as comprehensively about mathematics and statistics. Candidates will be qualified for lecturer positions in statistics and mathematics subjects in colleges and universities after completing the PhD Statistics course. They can work in educational institutions such as schools and universities as teachers and lecturers. Candidates with a PhD can become the most knowledgeable in their field of specialization. Part-time programs are also available for working professionals. After completing this program, students can expect to earn a good salary package of up to Rs. 8, 00, 000.

### Programs in Phd:

The highest educational degree in India is a PhD, thats a doctorate level degree. Following the completion of a PhD in statistics, most people do not continue their education. Moreover, there is high employability and graduates are rapidly hired in high-paying jobs after completing their degrees. There is no end to learning and knowledge with this knowledge. Following a PhD, one can pursue one of the following programs:

• Phil. Statistics: After completing a PhD in statistics, students can pursue an M Phil in statistics, which entails additional statistical research.
• Phil. Mathematics: After completing the PhD in Statistics program, students can pursue an M Phil in Mathematics.
• You can also continue your study as a Postdoctoral Fellow with CSIR and UGC fellowships after getting your doctorate degree in statistics.

## Statistics Job Roles and Levels in India

A candidate with a degree in this discipline has a wide range of work opportunities. Working for either the government or corporate companies and a variety of other sectors will be simple for them. They can also teach in colleges or universities as a professor or lecturer. In the field of statistics, there are numerous work prospects. Students upon completing their degrees can work in a variety of fields. They can become psychometrists and investment Analysts, as well as cryptologists and Commodities Traders Financial Aid Directors and Information Scientist, are also other professions available for them. Students can even pursue a career in education and become a professor. The research field is likewise very broad.

### Data Analysts: Beginner, Mid-Experienced and Highly Experienced

A Data Analyst collects and analyses data in order to find new ways to better businesses and government agencies. They are also responsible for analyzing and storing databases and their associated data. Any data such as that of labourers and clients as well as arrangements, and so on can include in this form of data. The data analysts – paid an average salary of Rs. 4, 00, 000 per annum.

Average Salary for Beginners: Rs. 4, 00, 000 LPA

Average Salary for Mid-Experienced: Rs.4 LPA to 10 LPA

Average Salary for Highly Experienced: Rs. 10 LPA to 20 LPA

### Economists: Beginner, Mid-Experienced and Highly Experienced

These specialists analyze and examine the information which has an impact on the government’s financial and money related jobs. They use this data for forecasting and clarifying economic tendencies. Economists use a variety of applications for analyzing and breaking down data. These also include the use of spreadsheets and factual examination as well as database management. Economists are paid an average salary of Rs. 6, 50, 000 per annum.

Average Salary for Beginners: Rs. 6, 50, 000

Average Salary for Mid-Experienced: Rs.4 LPA to 10 LPA

Average Salary for Highly Experienced: Rs. 10 LPA to 20 LPA

### Statisticians: Beginner, Mid-Experienced and Highly Experienced

They gather and display numerical data, assisting organizations in comprehending quantitative data and identifying patterns for making projections. The statisticians also devise techniques to overcome problems in data collection and analysis. Furthermore, they are paid an average annual salary of Rs. 3, 50, 000.

Average Salary for Beginners: Rs. 3, 50, 000

Average Salary for Mid-Experienced: Rs.4 LPA to 10 LPA

Average Salary for Highly Experienced: Rs. 10 LPA to 20 LPA

### Enumerators: Beginner, Mid-Experienced and Highly Experienced

An Enumerator is responsible for counting the number of people in a family, as well as recording their age and gender and other information. They gather and record this type of information. Enumerators earn an average annual salary of Rs. 6, 00, 000.

Average Salary for Beginners: Rs. 6, 00, 000

Average Salary for Mid-Experienced: Rs.4 LPA to 10 LPA

Average Salary for Highly Experienced: Rs. 10 LPA to 20 LPA

### Bio Statisticians: Beginner, Mid-Experienced and Highly Experienced

A biostatistician is a scientist who uses or applies arithmetic to progress research. In the field of agricultural business, biostatisticians prepare natural tests and gather and evaluate data. Thereafter they derive conclusions based on such data. Biostatisticians are offered an average annual pay of Rs. 7, 50, 000.

Average Salary for Beginners: Rs. 7, 50, 000

Average Salary for Mid-Experienced: Rs.4 LPA to 10 LPA

Average Salary for Highly Experienced: Rs. 10 LPA to 20 LPA

### Q1 What do you understand by the term Statistics?

• Statistics is a branch of mathematics concerned with the collecting, analysis, and interpretation of data, as well as its explanation and presentation. Statistics – sometimes seen as a distinct branch of mathematics rather than a subject of mathematics. While data employed in many scientific initiatives, statistics also deals with how to use data in uncertain scenarios and how to make conclusions in uncertain conditions.
• The identification and study of a population or process to researched the first step in applying statistics to a problem. In this usage, the population might refer to anything from “all the people living in a country” to “every atom in a crystal.” In general, statisticians collect data on the entire population, thats referred to as a census. Typically, government statistical institutes are in charge of this. Descriptive statistics can also use to summarize population data. Numerical descriptors such as mean and standard deviation are useful for continuous data (such as income). Frequency and percentage, on the other hand, better suited to categorical data.
• When a census not practicable, a sample of the population investigated and studied. As a result, data collected in the form of samples in an observational or experimental situation. Furthermore, thats only done once a representative sample of the total population has identified. Descriptive statistics may used to summarize the sample data. The numerical descriptors produced from the sample, however, ambiguous because the sample picked at random. To make meaningful inferences about the entire population, inferential statistics required.
• It relies on the patterns observed in the sample to draw conclusions about the population represented by the sample data. Conclusions may derived in the form of yes/no questions about the data (hypothesis testing) or by predicting numerical features of the data (estimation).
##### Inferences-
• Inferences include identifying data associations (correlation) and modelling relationships within the data (for example, using regression analysis). Forecasting and predicting, as well as estimating unknown variables in or related to the population under study, are all types of inference. Data mining, as well as extrapolation and interpolation of time series and spatial data, are instances of this.
• Therefore, statistics – the discipline of study that deals with data collection, organization, analysis, interpretation, and presentation. When using statistics for a scientific, industrial, or social problem, its typical to begin with a statistical population or model to research. The statistical population includes a diverse variety of people and objects, such as all citizens of a country or each atom in a crystal. Statistics is concerned with all elements of data, including the organization of data collecting in the form of experiments and surveys.
• When census data is unavailable, statisticians create specific experiment designs and sample surveys to collect data. This kind of representative sample also assures that the results and inferences reached can generalized to the full population. Experimental research, on the other hand, entails measuring and manipulating the system under consideration. Also, using the same technique, measure the new values to see if the change has changed the measures’ values. The observational study, on the other hand, does not require such an experimental change.
##### Two statistical methods are primarily used in data analysis-
• The first method, descriptive statistics, use indices such as the mean deviation and standard deviation. This method is used to summarize the data from the sample. The second way is inferential statistics, which uses data to draw conclusions and judgments. Unlike the descriptive method, however, this data is prone to random variation, such as observational mistakes and sample variance. Furthermore, descriptive statistics is a strategy that frequently deals with two sample or population distributional features. The central tendency, also known as the location property, describes the distribution’s core or typical value.

### Q2 Describe the historical back and importance of Statistics?

• Cryptographers and Arab mathematicians were the first to write statistical inferences and writings. Its during the Islamic Golden Age, which lasted from the seventh to the thirteenth centuries. The Book of Cryptographic Messages, composed by Al-Khalil (717–786), utilized the permutations and combinations for the first time. They used to count all of the possible Arabic words, both with and without vowels. In his book Manuscript on Deciphering Cryptographic Messages, Al-Kindi described how to use frequency analysis to decipher encrypted signals. Al-Kindi also credited with creating the first statistical decryption algorithms.
• Later, employing sample size, Ibn Adlan (1187–1268) made a substantial contribution to frequency analysis. The earliest European publication on statistics is John Graunt’s Natural and Political Observations touching the Bills of Mortality, published in 1663. The demand for states to adopt policies based on demographic and economic data prompted earlier statistical breakthroughs. The scope of the statistics disciplines broadened in the early nineteenth century to include data collecting and analysis in general. Statistics – now widely employed in both the public and private sectors, as well as in the social sciences.
• The mathematical roots of contemporary statistics formed with the introduction of probability theory by Gerolamo Cardano, Blaise Pascal, and Pierre de Fermat in the seventeenth century. The issue of probability had already addressed in mediaeval law and by philosophers such as Juan Caramuel. The probability theory of mathematics, on the other hand, arose from the study of games of chance. In the year 1805, Adrien-Marie Legendre was the first to define the least-squares approach.
• The field of statistics as we know it now arose in the latter half of the nineteenth and early twentieth centuries.

#### Contributions-

• Francis Galton and Karl Pearson’s contributions resulted in the development of statistics as a mathematical subject. Following that, statistics used to analyse data in a variety of fields, including science, industry, and politics. In addition, around the turn of the century, its the leader of the first wave. Galton’s contributions include the development of standard deviation concepts as well as correlation and regression analysis. It also includes the use of the aforementioned in the research of a variety of human characteristics, such as height and weight.
• Pearson – credited with inventing a number of things, including the Pearson product-moment correlation coefficient, thats defined as a product-moment. He also created the Pearson distribution method and the method of moments for fitting distributions to samples. Galton and Pearson contributed to the first publication of mathematical statistics and biostatistics (then known as biometry), called Biometrika. Pearson also founded the world’s first university statistics department at University College London.
• Between 1910 and 1920, William Sealy Gosset sparked the succeeding wave, which culminated in Ronald Fisher’s findings. He also wrote textbooks that were used in institutions all around the world to define the academic subject. His important 1918 study The Correlation between Relatives on the Supposition of Mendelian Inheritance (which for the first time utilized the statistical term variance) significant work. Statistical Methods for Research Workers, published in 1925, and The Design of Experiments, published in 1935, were among his most notable contributions.
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• He created the concepts of sufficiency and supplemental statistics, as well as Fisher’s linear discriminator and information. The principle of Fisher (called “probably the most celebrated argument in evolutionary biology” by A. W. F. Edwards). Fisherian runaway, a concept in sexual selection about positive feedback runaway effect seen in evolution, one of the biological topics he applied statistics to. The combined work of Egon Pearson and Jerzy Neyman in the 1930s resulted in the final wave, which mostly consisted of refining and developing previous breakthroughs.
• They went over words like “Type II” error, test power, and confidence intervals. Jerzy Neyman established in 1934 that random sampling was a better method of an estimate than purposive (quota) sampling. Statistical methods currently applied in every industry that requires decision-making. They also used for obtaining valid inferences from a vast body of data and making decisions in ambiguous scenarios utilizing statistical methods. Modern computers have sped up large-scale statistical computations and allowed the introduction of novel processes that would have been hard to implement manually.

### Q3 Explain the different types of Statistics?

• Statistics is a mathematical method of evaluating, analyzing, and summarizing data. As a result, descriptive and inferential statistics can be classified based on their properties. Based on how data represented, we analyze and evaluate it. This accomplished through the use of pie charts, bar graphs, and tables. Statistics – a subject of mathematics thats originally considered the science of many different types of statistics. For example, the collection and analysis of data on a country’s economy and population. Also, its military, literacy, and other aspects. Linear algebra, stochastic analysis, differential equations, and measurement are all covered in statistics.
• In its most basic form, statistical analysis used to collect and analyze large volumes of data. Statistics is a branch of mathematics that involves the computation of vast amounts of data utilizing charts, tables, and graphs. The data collected for analysis referred to as measurements in this context. We now draw a sample from the population if we need to measure data based on a scenario. After that, the analysis or computation for the next measurement completed.
• Descriptive statistics: In this type of statistics, the data summary created utilizing the required observations that have previously provided. The summary is a representation of a population-based on a sampling of the population. Furthermore, the mean and standard deviation parameters used. Descriptive statistics is a way of organizing, displaying, and summarizing a set of data using tables and graphs, as well as summary metrics. This strategy, for example, can used to collect data on a group of people in a city who use the internet or watch television.

#### There are four different types of descriptive statistics:

• Frequency measurement
• Measurement of dispersion
• Measuring the central tendency
• The measurement from a certain location
• The frequency of a piece of data determined by counting how many times it appears. Range and variance, as well as standard deviation, used to calculate dispersion. It determines how widely information is transmitted. The mean, median, and mode of the data describe the data’s central tendencies. The position measurements describe the percentile and quartile ranks.
• Inferential statistics: Inferential statistics used to interpret the meaning of descriptive statistics. To put it another way, we use statistics to grasp the relevance of the data we’ve collected, analyzed, and summarized. To put it another way, its used to make inferences from data that are prone to random changes such as observational errors and sample variation, among other things. Inferential statistics is a method of using sample data to make judgments, predictions, and conclusions about a population. It enables us to make statements that go beyond the data or information thats now available. Estimates based on hypothetical research and studies are examples of inferential.

### Q4 What are the different undergraduate and postgraduate courses available in the Statistics discipline?

• Statistics – a mathematical field thats often used in data analysis and research. Statistics is a subject that can be studied at any level of education, including certificate and diploma programs. They also offer post-graduate diplomas and undergraduate, postgraduate, and doctoral degree programs. In addition, certificate and diploma programs are popular options for learning the subject. These courses are available both online and offline. This allows students to complete their coursework while working full-time. Several of these statistics certificate courses are available for free.

#### B Sc.:

• The Bachelor of Science in Statistics (B. Sc. Statistics) is a three-year undergraduate program in statistics that covers topics including probability and statistical methods. Similarly, this research includes survey sampling and numerical analysis. Lectures, as well as flight and simulation training, included in the course. This curriculum also includes assignments and other activities aimed at giving both classroom and practical education. Students who want to pursue a B. Sc. in Statistics must have completed grades 10+2. They must have taken physics and chemistry classes in addition to math.
• A minimum of a 50% grade from a recognized Indian school required for B. Sc. Statistics admission. Admissions to top colleges in India that offer B. Sc. degrees are based on merit. They also take into account the results of entry exams such as the GSAT and BHU UET, as well as the IISER IAT. A B. Sc. Statistics degree typically costs between Rs. 20, 000 and Rs. 1,50,000 per year. This industry expected to generate more than 20 lakh jobs in the next five years. A course typically costs between Rs. 20, 000 to Rs. 1,50,000. Students who complete this degree put in positions such as risk analyst, statistician, and actuary manager.

#### M Sc.:

• A postgraduate program in statistics called M. Sc. Statistics (Master of Science in Statistics) is available. Its all about figuring out how data acquired, organized, and evaluated. It covers a wide range of topics, including data collection planning and survey and experiment design. The average M. Sc. Statistics program lasts two academic years, but this varies by institute. Candidates who want to pursue this degree must have a bachelor’s degree in mathematics or statistics. They can also hold a related bachelor’s degree from a recognized university. Its the list of eligibility requirements for applying to this program.
• The majority of M. Sc. Statistics students admitted to their programs after passing an entrance exam. However, a few colleges do admit students based on their academic merit. An M. Sc. in Statistics costs anywhere between Rs. 5,000 and Rs. 65,000 in India. This course will teach you how to address real-world statistical problems. The M. Sc. Statistics curriculum includes topics like computational statistics and statistical machine learning, as well as the fundamental principles of statistical inference.
• Graduates of M. Sc. statistics work in consultancies, analyzing people’s preferences and habits. Marketing, finance, and data metrics are some of the other professions available. Successful M. Sc. Statistics postgraduates in India earn an average annual salary of Rs. 3,00,000 to Rs. 7,00,000. After completing the MSc Statistics course, a candidate might pursue additional study and research in this field. They can work as college teachers after earning a doctorate in statistics.

### Q5 Explain the doctoral degree in Statistics and also mention the options available after this PhD degree?

• A PhD in statistics = a two-year doctoral program in statistics thats pursued after completing a Master’s degree. This PhD program focuses on the collection, analysis, interpretation, and presentation of numerical data, thats a part of mathematics. This program aids in the determination of measuring system variability and data bridging control processes. In addition to making data-driven decisions. This program covers a wide range of academic areas, from physical science to humanities and social sciences. In the discipline of statistics, both mathematical and applied statistics are studied. To consider a candidate for this program, candidates must have completed an M. Sc. or M. A. in mathematics or statistics with a grade point average of at least 55 per cent.
• The candidate’s performance on the postgraduate degree test will determine admission to the PhD statistics program. It could also determined by their performance on the institution’s entry examinations. Graduates of PhD. statistics work as Research Analysts, Assistant Professors, and Data Analysts. They can also work as Biostatisticians, Data Interpreters, and Research Scholars, among other things. Also, they work in Statistical Services, Social Research, and Economics and Finance, among other subjects. In addition to this, they work in India’s economic services, businesses, and commerce, as well as government jobs, consulting firms, and other industries.

#### Fees-

• The typical annual tuition cost for this program in India is between Rs. 10,000 and Rs. 1,50,000. In India, a PhD Statistics degree holder’s average annual pay ranges from Rs. 3,00,000 to Rs. 8,00,000 per year. If students wish to pursue more research, they can continue as independent researchers and have their research papers published. These students can also pursue an M Phil in mathematics or an M Phil in statistics. They may also pursue a D. Sc. (Doctor of Science) degree in the relevant field in the future.
• The PhD in Statistics an excellent research-based analytic program for those interested in broadening their knowledge and expertise. This training improves one’s numerical data gathering, analysis, and interpretation skills, as well as presentation skills. Candidates’ research may contribute to the advancement of statistics. Changes in paperwork and regulation, as well as training and technology, used to accomplish this. Its a broad academic area that includes everything from the humanities to the physical and social sciences. In the discipline of statistics, both mathematical and applied statistics are studied. Furthermore, descriptive statistics and inferential statistics are two types of applied statistics to study.
• The goals and objectives of each individual will determine whether or not they pursue a PhD in statistics. Students who complete the Statistics course prepared for careers in academia, government, and non-profit organizations. They also teach children to think critically and creatively about mathematics and statistics, as well as thoroughly. After completing the PhD Statistics program, candidates will be qualified for lecturer jobs in statistics and mathematics at colleges and universities. They can work as teachers and lecturers in educational institutions such as schools and universities.

#### PhD-

• Candidates with a PhD are likely to be the most knowledgeable in their field. Working professionals can also enrol in part-time programs. Students can expect to earn an excellent salary package of up to Rs. 8,00,000 after completing this program.
• A PhD, or doctorate level degree, is the highest educational degree in India. The majority of people do not continue their education after completing a PhD in statistics. Furthermore, graduates have a high employability rate, and after completing their degrees, they quickly hired in well-paying employment. With this information, there is no limit to what you may learn and know. One can pursue one of the following programs after earning a Ph. D.
• Statistics for an M Phil: Students can pursue an M Phil in statistics after completing a PhD in statistics, which entails additional statistical research.
• Phil. Mathematics: Students can pursue an M Phil in Mathematics after completing the PhD in Statistics program.
• After earning your doctorate in statistics, you can apply for CSIR and UGC scholarships to continue your studies as a Postdoctoral Fellow.
List of Universities offering Statistics
List of Universities