This mathematics and statistics group includes all classes of positions, the duties of which are to advise on, administer, supervise, or perform research or other professional and scientific work or related clerical work in basic mathematical principles, methods, procedures, or relationships, including the development and application of mathematical methods for the investigation and solution of problems; the development and application of statistical theory in the selection, collection, classification, adjustment, analysis, and interpretation of data; the development and application of mathematical, statistical, and financial principles to programs or problems involving life and property risks; and any other professional and scientific or related clerical work requiring primarily and mainly the understanding and use of mathematical theories, methods, and operations.

There were **18,642 employed in this group** including 60 that work overseas. The largest employers are the Departments of the Army, Navy, and Air Force employing 9,743 civilians in the GS-1500 group followed by the Department of Commerce with 3,030 and the Department of Agriculture with 779. All cabinet level agencies and a few large independent agencies including NASA employs workers from this group.

The following information is compiled from numerous federal documents including qualification standards, job announcements, career articles, occupation flysheets, FEDSCOPE, OPM, Agency web sites, interviews with federal employees, The United States Government manual, and from the Department of Labor’s Occupational Outlook Handbook.

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These position descriptions are excerpted from the qualification standards for select job titles in this group. In the General Schedule position classification system is established under chapter 51 of title 5, United States Code. The term “General Schedule” or “GS” denotes the major position classification system and pay structure for white collar work in the Federal government. Agencies that are no longer subject to chapter 51 have replaced the GS pay plan indicator with agency-unique pay plan indicators. For example, the Bureau of Prisons uses GL instead of the GS designation. For this reason, reference to General Schedule or GS is often omitted from the individual qualification standard sheets.

A brief introduction for major occupations within this group is provided below.

Actuaries manage, supervise, lead, or perform scientific work in the field of actuarial science. Actuarial science involves professional knowledge of the disciplines of mathematics, statistics, business, finance, economics, and insurance. The work requires applying this knowledge to programs or problems related to the financial risks posed by life, health, retirement/pension, and property/casualty entities and contingencies.

**The federal government employs 289 actuaries. **The Pension Benefit Guaranty Corporation employs the largest number with 92 followed by Health and Human Services with 61, the Treasury Department with 27 and OPM employs 15.

Actuaries in the Federal Government evaluate the financial status of Federal programs designed to help protect individuals, businesses, and pension plans against adverse financial contingencies. They also play an active role in designing, modifying, and administering these Government programs and in providing the facts and estimates that serve as the foundation for management decisions and actions in administering these programs.

**Job Series Titles: **

- USAJOBS GS-1510
**(Actuary****Federal Job Lists)** - Private Sector Job Listings

This series covers positions that manage, supervise, lead, or perform scientific work that involves designing, developing, and adapting mathematical, statistical, econometric, and other scientific methods and techniques. The work also involves analyzing management problems and providing advice and insight about the probable effects of alternative solutions to these problems. The primary requirement of the work is competence in the rigorous methods of scientific inquiry and analysis.

**The federal government employs 4,789 operations research analysts** of which 36 work overseas. The Departments of the Army, Navy, and Air Force employ 3,432 civilians followed by the Department of Defense with 503 and the Department of Transportation with 238. All cabinet level agencies and a few small agencies employ Operations Research Analysts.

Analysts usually deal with a variety of broad issues, subject matter areas, and problems. Each assignment presents a different question. Over time, analysts may gain considerable knowledge of some specialty fields, yet operations research knowledge remains paramount. Analysts often borrow and adapt analytical methods and modify techniques from other scientific, technical, and analytical disciplines. Similarly, professionals in other fields may use the operations research approach to solve problems in their disciplines.

The analytical process has four phases: problem definition, model development, hypothesis testing and investigation, and predictions/explanations.

**Job Series Titles: **

- USAJOBS GS-1515
**(Operations Research Analyst****Federal Job Lists)** - Private Sector Job Listings

Mathematicians manage, supervise, lead, or perform scientific work that involves researching on basic mathematical principles, methods, procedures, techniques, or relationships, They also may develop mathematical methods to solve a variety of scientific, engineering, economic, and/or military problems where precise specification of the relationships, rigor and economy of mathematical operations, and logical deduction are the controlling considerations.

**The federal government employs 1,000 mathematicians. **The Departments of the Army, Navy and Air Force employs 820**.** The Commerce Department employs 50, the Department of Health and Human Services employs 30, and the National Science Foundation employs 28.

Traditionally mathematics consists of two generic types of work: pure or abstract mathematics, and applied mathematics.

- Pure or Abstract Mathematics – is sometimes referred to as basic research. Relatively few mathematicians perform basic research. This work involves studying and developing principles for their own sake and possible future rather than immediate usefulness.
- Applied Mathematics – concerns mathematical aspects of the physical, natural, and social sciences. In a restricted sense, the term refers to using mathematical principles as tools in the fields of physics, chemistry, engineering, biology, and the social sciences.

**Job Series Titles: **

- USAJOBS GS-1520
**(Mathematician Federal Job Lists)** - Private Sector Job Listings

This series covers positions that manage, supervise, lead, or perform:

- scientific work that involves designing, developing, and adapting mathematical methods and techniques to statistical processes; or
- research that relates to the basic theories and science of statistics.

**The federal government employs 1,441 mathematical statistician **of which 1 works overseas. The largest employer is Health and Human Services with 565 followed by the Department of Commerce with 381 and the Department of Agriculture with 148. All cabinet level agencies, except for the State Department, hire in this group. There are also opportunities for employment at some large independent agencies such s the EPA that employs 24 mathematical statisticians.

Mathematical statisticians perform duties in which the “problem” is the basic work unit. The size and complexity of the problem varies extensively. Solving a problem usually requires that the mathematical statistician use standard research procedures. These procedures, sometimes referred to as the scientific method, include the following seven basic work processes:

- defining problems;
- conducting background research;
- planning;
- conducting investigations;
- reducing findings to facts;
- interpreting findings; and
- documenting findings.

The science of mathematical statistics is a body of theories and methods for obtaining knowledge. Mathematical statisticians do not merely rely on a collection of facts; instead they are characterized by the techniques that they develop to design models for collecting quantified data.

**Job Series Titles: **

- USAJOBS GS-1529
**(Mathematical Statistician****Federal Job Lists)** - Private Sector Job Listings

This series covers positions that manage, supervise, lead, or perform scientific work or provide professional consultation in applying statistical theories, techniques, and methods to gather, analyze, interpret, and/or report quantified information.

**The federal government employs 3,127 statisticians **of which 1 works overseas. The largest employer is Health and Human Services with 565 followed by the Department of Commerce with 381 and the Department of Agriculture with 148. All cabinet level agencies, except for the State Department, hire in this group. There are also opportunities for employment at some large independent agencies such as the EPA that employs 24 mathematical statisticians.

**Job Series Titles: **

- USAJOBS GS-1530
**(Federal Job Lists)****Survey Statistician****Statistician**

- Private Sector Job Listings

Survey Statistician are primarily concerned with:

- overall planning or executing complete surveys of any size, or parts of large surveys, including initial negotiations or development of the survey; and
- establishing general specifications and detailed time schedules that govern the following:
- data content, collection, and dissemination;
- instrument design;
- analysis; and
- modifying systems design.

The title Statistician is used when the work of the position does not satisfy the criteria for use of the title Survey Statistician.

**Survey Statisticians**

A survey is a scientific method of gathering information from a sample of individuals, households, firms, institutions, or other units of analysis so that results can be generalized to the entire population. The validity of survey results depends on selecting the sample so that each unit has a measurable chance of selection and collecting information using standardized, replicable procedures. Survey statisticians apply statistical theories and techniques to:

- plan, organize, and operate programs for collecting, verifying, adjusting, processing, summarizing, analyzing, and presenting information numerically; and
- conduct research to evaluate data quality.

Survey statisticians collect primary data from original sources and secondary data from records, instruments, or reports established for historical, administrative, regulatory, or quality control purposes. They also select or sample data.

**Statisticians**

Statisticians may use data derived from a probability sample. They are usually responsible for the design, size, and characteristics of the probability samples that are necessary to ensure the reliability of data.

Statisticians may provide advice or be directly involved in collecting primary data. They examine data collected by others to help them understand its implications and limitations for the problem under study. Further, statisticians evaluate data collection and statistical methodologies, and develop better data collection methods.

Statisticians organize data into a format that facilitates the required analysis and communicates the results to data users. The organization of data takes different forms depending upon the problem under investigation. For example, if one is interested in changes over time, statisticians present the data in a different manner than when one is interested in the current period’s totals. The problem may involve comparing data easily with masses of similar data and analyzing differences, or developing complex models to support in-depth analysis of data, illustrate and interpret findings, and disseminate findings to a variety of constituents.

This series includes positions which require primarily the application of knowledge of statistical methods, procedures, and techniques, to the collection, processing, compilation, computation, analysis, editing, and presentation of statistical data. The work does not require the application of professional knowledge of statistics or other disciplines.

**The federal government employs 1,017 statistical clerks and assistants **of which 2 work overseas. The largest employer is the Department of Commerce with 790 followed by the Department of Agriculture with 69 and the Department of the Army with 43. Many cabinet level agencies hire in this group.

**Job Series Titles: **

- USAJOBS GS-1531
**(Federal Job Lists)****Statistical Clerk GS-3/4****Statistical Assistant GS-5/9**

- Private Sector Job Listings

A great deal of the statistical information collected by agencies in the Federal Government can be presented satisfactorily by elementary numerical treatment, such as by giving ratios, percentages, averages, etc. In many areas of Government operations, however, more intricate and refined methods must be used, e.g., measures of dispersion, frequency distribution, time series analyses, index numbers, correlations, sampling, etc. This is particularly true where it becomes necessary to compare significant differences among groups, establish the reliability of data obtained in a sample, or measure the validity of the relationships of data between and among the different groups being studied, surveyed, or analyzed.

Many of the methods, procedures, and techniques involved, being essentially basic forms of statistical analysis, require the application and use of various equations and formulas. These are developed by statisticians, who apply mathematical and statistical principles in deciding what equation or formula is appropriate.

The extent to which any method, procedure, or technique is used varies from one organization or agency and from one study or project to another. This depends to a large extent upon the impact and effect of several variables. These include the nature of the statistical functions involved, the purpose and use of the data, the degree of refinement and accuracy required in a specific study or operation, the anticipated impact of the results on subsequent studies, and the specific requirements set by the statisticians, program or subject-matter specialists, and other interested operating officials.

In much of the work, the statistical methods, procedures, and techniques can be and are reduced to relatively simple components. These, in turn, are translated into a series of sums, quotients, roots, etc., that are determined by addition, subtraction, multiplication, and division, and by selection and comparison on that basis. Where this is done, the work resolves itself to a greater or lesser degree into computing procedures that combine these mathematical techniques in particular sequences. This, and the development of new equipment and methods designed to retrieve previously recorded data stored on tapes and in memory chambers, is the basis for automating many statistical operations. As a result, much of the statistical work, particularly in the larger operations where it can be standardized sufficiently, is performed by coding clerks, card punch operators, and computer specialists.

Cryptanalysts study and analyze data and information systems to study the underlying hidden aspects of systems. Cryptanalysis is used to break into cryptographic security systems to uncover the contents of the encrypted message.

**The federal government employs 18 cryptanalysts. **All work for the Department of Justice. **Note:** Employment in this group may also be available at agencies such as the CIA, FBI, and other agencies that are not required to report their employment statistics.

Use the Group Coverage Qualification Standard for Technical and Medical Support Positions for this series in conjunction with the Individual Occupational Requirements described below.

**Individual Occupational Requirements**

**Specialized Experience** (for positions at GS-4 and above): Experience must have been in a specific branch of the physical sciences such as physics, chemistry, geology, or metallurgy, or mathematics.

or

**Education and Training**

- For GS-3: Successful completion of 1 year of study that included at least 6 semester hours of courses in the physical sciences or mathematics.
- For GS-4:Successful completion of 2 years of study that included at least 12 semester hours in the physical sciences or mathematics.
- For GS-5: Successful completion of a full 4-year course of study leading to a bachelor’s degree that included major study or at least 24 semester hours in the physical sciences or mathematics.

**Job Series Titles: **

- USAJOBS GS-1541
**(Cryptanalysis****Federal Job Lists)** - Private Sector Job Listings

Computer scientists include professional positions which primarily involve the application of, or research into, computer science methods and techniques to store, manipulate, transform or present information by means of computer systems. The primary requirements of the work are (a) professional competence in applying the theoretical foundations of computer science, including computer system architecture and system software organization, the representation and transformation of information structures, and the theoretical models for such representations and transformations; (b) specialized knowledge of the design characteristics, limitations, and potential applications of systems having the ability to transform information, and of broad areas of applications of computing which have common structures, processes, and techniques; and (c) knowledge of relevant mathematical and statistical sciences.

**The federal government employs 6,746 computer scientists **of which 19 work overseas. The Departments of the Army, Navy, and Air Force employ 5,229 civilians followed by the Department of Defense with329 and the Department of Health and Human Services with 259. Most cabinet level agencies and a few large independent agencies such as NASA employ computer scientists.

Computer scientists in the Federal service develop new and improved concepts, principles, and techniques that will advance the body of knowledge of computer science, and adapt and apply advanced computer science methods and techniques to solve complex computer processing requirements.

**Job Series Titles: **

- USAJOBS GS-1550
**(Computer Scientist Federal Job Lists)** - Private Sector Job Listings