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Essential skills profile

This profile contains a list of example tasks that illustrate how each of the 9 essential skills is generally performed by most workers in this occupation. The levels of complexity estimated for each task are ranked between 1 (basic) and 5 (advanced).

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Mathematicians, Statisticians and Actuaries(2161)

Mathematicians and statisticians research mathematical or statistical theories, and develop and apply mathematical or statistical techniques, for solving problems in such fields as science, engineering, business and social science. Actuaries apply mathematics, statistics, probability and risk theory to assess potential financial impacts of future events. Mathematicians, statisticians and actuaries are employed by universities, governments, bank and trust companies, insurance companies, pension benefit consulting firms, professional associations and science and engineering consulting firms.

Reading Help - Reading
  • Read short comments, explanations and instructions on forms. For example, a statistician may locate inconsistencies in responses to control questions on survey forms. (1)
  • Read e-mail from co-workers, colleagues and clients. For example, they may read e-mail from colleagues scheduling and confirming meeting arrangements, asking for information and responding to questions about joint projects. (2)
  • Read magazines and bulletins to stay abreast of technological advances, legislative changes and other matters affecting their work. For example, an actuary may read a news article posted on the Canadian Institute of Actuaries' web site to learn about recent changes to the standards of practice for actuarial evidence. A mathematician may read a bulletin posted on the Centre de recherches mathématiques' web site to learn about an upcoming workshop on advanced mathematical techniques. (3)
  • Read instruction manuals, 'help' items and 'frequently asked question' entries when operating computers and peripheral equipment. For example, a statistician may read a manual to review the steps needed to perform non-linear modelling and to draw three-dimensional graphs of mathematical functions. An actuary may read help items to review the steps needed to program a retirement plan's benefit provisions. (3)
  • May read requests for proposals for projects which involve the research, development and application of mathematical theories and techniques to solve scientific, engineering, financial, management and socioeconomic development problems. They read proposal requests to learn about the scope of proposed work, mandatory requirements for credentials and experience, evaluation criteria and selection processes and to determine whether they have the necessary skills and resources to undertake the projects. (4)
  • May read legislation to verify rules and regulations and provide advice to co-workers, colleagues and clients. For example, actuaries may review the Insurance Companies Act, the Income Tax Act, the Pension Benefits Regulations and other superannuation, compensation and insurance legislation when designing life, health and property insurance policies, and pension and superannuation plans. They may select and integrate information from a number of acts to provide legal evidence on the value of premiums, contributions, benefits and future earnings. (4)
  • Read a wide range of academic journals such as the Journal of the American Mathematical Society, the Canadian Journal of Statistics and the North American Actuarial Journal. They select and read relevant articles to expand their knowledge of mathematical, statistical and actuarial theories and techniques. They also refer to these articles when creating research plans, developing their own theories and techniques and searching supportive evidence for recommendations. (5)
Document use Help - Document use
  • Scan product and file labels for data such as sizes, dates and serial numbers. (1)
  • Enter data into tables. For example, a demographer may enter data on age, gender, family structure, income and educational attainment into tables to study the determinants for access to post-secondary education. An actuary may enter probability rates for fires, natural disasters, thefts, car accidents, illnesses and deaths into tables to determine insurance premiums. (2)
  • Locate data in lists and tables. For example, a mathematician may read a list of bibliographical references at the end of a journal article to identify other articles relevant to a research topic. A statistician may locate data on single parent families in tables drawn from Statistics Canada research. (2)
  • Complete forms. For example, research mathematicians and statisticians may complete grant application forms. Actuaries may complete government forms to amend registered pension plans on behalf of clients. They may collect and enter data such as the names of additional employers participating in the plans, the numbers of employees starting and ceasing to participate under the plans and other amendment details. (3)
  • Locate data in forms. For example, an actuary may review tax forms completed by clients to locate the total values of accrued liabilities. (3)
  • Interpret graphs. For example, an actuary may interpret a graph to estimate the future deficits of a retirement benefit plan. A biostatistician may interpret a cluster graph to analyse the results of complex gene micro-array experiments. (4)
  • Interpret schematic drawings. For example, a mathematician may study electrical schematics to infer equations describing an electrical engineering design. An epidemiologist may interpret a schematic illustrating a health management model. A statistician may review schematics describing survey data structures. (4)
Writing Help - Writing
  • Write short comments on forms. For example, research mathematicians and statisticians may write brief descriptions of projects on the cover pages of grant application forms. (1)
  • Write e-mail to co-workers, colleagues and clients. For example, a research mathematician may write e-mail to peers to solicit their expertise on convex functions. An actuary may write a short message to respond to a client's enquiries about a pension plan. (2)
  • Write letters to colleagues, clients, research subjects and individuals from various organizations and government departments. For example, an epidemiologist may write a letter to participants in a research project on post-stroke rehabilitation to inform them about the benefits of the research, consent procedures, risks, inconveniencies, confidentiality, right to withdraw and compensation. An actuary may write a letter to an official at the Treasury Board of Canada Secretariat to request acceptance of amended actuarial practices for the delivery of pension commuted values. (3)
  • May write survey items and questionnaires used to collect data. They must be explicit and precise to reduce ambiguity and to ensure that survey participants do not misinterpret questions. For example, a demographer may develop a survey questionnaire to collect data on community access to the Internet. A statistician may write a survey questionnaire to collect annuitants' views on a direct deposit pay system. (3)
  • Prepare policies, procedures and guidelines. For example, an actuary may write pension, group and retirement benefit plans or life, property and health insurance policies. A demographer may write procedures for merging area-level census data with survey data in Statistics Canada Research Data Centres. (4)
  • Write lengthy proposals for projects which involve the research, development and application of mathematical theories and techniques to solve scientific, engineering, financial, management and socioeconomic development problems. In these proposals, they address project objectives and convey complex concepts. They identify project team members and describe their academic backgrounds and relevant work experiences. For example, an operations researcher may prepare a research proposal for the development of a multiple criteria optimization algorithm which will be used to support negotiation processes. (4)
  • Write reports for employers, clients and research funding organizations. In these reports, they describe projects' backgrounds, objectives and methodologies, discuss findings and offer conclusions and recommendations. They may also edit and rewrite research reports so that they can be easily understood by the general public. For example, an actuary may write a report justifying changes to rates and reserve valuations. A biostatistician may write on the measured cellular responses of spruce trees and poplars to specific treatments and a demographer may write on interregional migration in Canada. (4)
  • May write articles for scientific journals, conference proceedings and research publications. They summarize research protocols, outline difficulties encountered in conducting experiments, discuss mathematical principles used to analyse data, present results obtained and explain their significance. For example, a mathematician may write an article on geometric matching for a conference on computational geometry. An operations researcher may report on the topological design of two-level telecommunications networks with modular switches. A biostatistician may write on the development of algorithms for genetic research. (5)
Numeracy Help - Numeracy Money Math
  • Calculate travel claims upon return from out-of-town project meetings, conferences, seminars, symposia, workshops and courses. They calculate reimbursements for use of personal vehicles at per kilometre rates and add amounts for accommodation, meals and other expenses. (2)
  • May calculate purchase order and invoice amounts. They calculate line amounts, taxes and totals on purchase orders for capital expenditures such as computer equipment acquisitions. When preparing invoices for project work, they may multiply numbers of days worked by daily rates, add costs of printing, courier services, proofreading and other subcontracted work, calculate applicable taxes and total amounts. (3)
Scheduling, Budgeting & Accounting Math
  • May calculate values of assets and liabilities. For example, an actuary may calculate an insurance company's short-term and long-term liabilities to ensure sufficient funds are available to meet claim commitments. (4)
  • Prepare schedules for large and complex projects, programs and services. For example, a statistician may use a critical path algorithm to prepare a schedule for the design, implementation and analysis of a longitudinal survey of immigrants to Canada. An operations researcher may apply an optimization algorithm to prepare train schedules and routes, and reduce transit times. (5)
  • Prepare budgets for large and complex projects, programs and services. For example, actuaries may prepare budgets for employers' contributions to pension, benefit and insurance plans. They calculate pension and benefit plan contributions and life, health, property, social and casualty insurance premiums using various economic and demographic assumptions. (5)
Measurement and Calculation Math
  • May create mathematical methods to measure the values of various parameters during experiments. For example, they may create indices to measure quality of life and foliar damage to trees. They may create methods for mapping cancer growth and for monitoring changes in species composition, solar radiation, acid deposition, precipitation, air pollution and water quality. (4)
  • Measure physical properties using advanced mathematical techniques. For instance, a mathematician may apply principles of algebra, geometry and topology to create a robotic librarian able to read press articles and to group them by language and context. This involves converting written words into polytopes with near-infinite dimensions. (5)
Data Analysis Math
  • May determine sample sizes and sampling methods for statistical research. They may calculate numbers of sample survey participants required to adequately represent target groups by demographical characteristics such as geography, age, sex, family structure, education, employment status and income. For example, a statistician may use a stratified sampling technique to determine the number of survey participants needed in each stratum of a national sample survey of graduate students. (4)
  • Investigate covariance, correlation and causation. For example, a biostatistician may perform genetic linkage analyses to identify chromosomal regions with genes that influence complex human traits such as intelligence. (4)
  • Create mathematical tools and models to ensure the efficient utilization of materials, equipment and resources. For example, an operations researcher may use an optimisation algorithm to calculate the medical equipment and supply inventories needed to ensure adequate patient service in the emergency unit of a hospital. An actuary may develop and apply stochastic models to analyse stock markets and interest rates and recommend ideal portfolio structures. (5)
  • Apply probability theories and create statistical methods to collect, analyse, interpret and display research data which will support public and private sector decision making and policy development. For example, a demographer may collect, analyse, interpret and display research data on post-secondary enrolments, tuition fees and demographical characteristics to facilitate policy development. An actuary may collect, analyse, interpret and display statistics of deaths, sicknesses, disabilities, car accidents and other phenomena to assist an insurance company in assessing risks, developing financial policies and making plan coverage decisions. (5)
Numerical Estimation
  • May estimate the number of additional trials required to obtain valid statistical measures. They must consider many factors and achieve a considerable degree of precision to ensure the scientific validity of results. (3)
  • Estimate costs and benefits. For example, an actuary may apply probability and risk theory principles to estimate the expenditures to be generated by group benefit and retirement benefit plans and their expected outcomes using different retirement age, death age, turnover and monthly contribution scenarios. Many factors are involved in these estimates and the factors themselves may need to be estimated. (4)
  • Estimate the short and long-term effects of various phenomena. For example, a mathematician may design an age-structured model to estimate the long term effects of haematological diseases in human subjects. A biostatistician may create a 'core of disease' model to estimate how a type of flu will spread through a heterogeneous population. (4)
Oral communication Help - Oral communication
  • Talk to suppliers about product performances, price quotes and delivery times. For example, a biostatistician may talk to micro-array suppliers to obtain price and shipping information. An actuary may speak to pension fund providers to enquire about funds' performances. (1)
  • Discuss project priorities, methodologies, schedules, progress, findings, problems faced and solutions found with their managers and clients and obtain guidance, recommendations and approvals. For example, a statistician may discuss survey objectives, questionnaire design and data collection with a client. (2)
  • May provide direction and advice to co-op students and junior mathematicians, statisticians and actuaries and review completed tasks and help resolve difficulties. For example, operations researchers may discuss the analysis of historical recruitment, promotion, retirement and separation data with co-op students as they can prepare the probability tables needed to test human resources planning models. (3)
  • Advise co-workers and colleagues from other disciplines on the application of mathematical, statistical and actuarial theories and techniques. For example, a biostatistician may advise laboratory technicians on the measurement of cell responses. An actuary may advise information technology department technicians on procedures for data mining. (3)
  • Contribute to meetings and conference calls with co-workers and colleagues. At these meetings, they discuss the coordination of job tasks and share information on research findings, legislative changes, technological advances and other matters affecting their work. They may also present mathematical, statistical and actuarial theories and techniques they have developed and applied to solve scientific, engineering, financial, management and socioeconomic development problems. (3)
  • Present project findings and recommendations to clients and managers. For example, an actuary may present a proposed pension plan to a client's executive staff. (4)
  • Present information on mathematical theories and procedures to colleagues at seminars and conferences. For example, a mathematician may present a workshop on solutions to Bolza problems to colleagues at an international conference. A statistician may deliver a presentation on the socioeconomic factors affecting the supply of professors to groups of college and university representatives. (4)
Thinking Help - Thinking Problem Solving
  • Realize that they will miss project deadlines because of missing, inadequate and inaccurate data. They meet project managers and clients to review project plans and negotiate new deadlines. (2)
  • Are unable to source software, equipment and personnel needed for ongoing work. For example, they may be unable to find Canadian sources for specialized software. They search the Internet and find several foreign manufacturers able to supply the software. They meet with their purchasing departments to discuss software functions, identify appropriate suppliers and arrange for the fastest possible delivery methods. (3)
  • Receive complaints from managers and clients who are unsatisfied with work they have delivered. They review their work, change it in light of the comments and suggestions received and resubmit it for approval. They may have to change the orientation of their work to satisfy managers and clients. For example, statisticians may receive complaints about survey questionnaires which they have written. Actuaries may receive complaints about life, health and property insurance policies, and pension and superannuation plans which they have designed. (4)
Decision Making
  • May select tasks to assign to co-op students, junior mathematicians, statisticians and actuaries. They consider individual academic backgrounds, skills, experiences, strengths, weaknesses and availabilities. (2)
  • Decide to participate in specific projects which involve the research, development and application of mathematical theories and techniques to solve scientific, engineering, financial, management and socioeconomic development problems. They review requests for proposals, identify project tasks and requirements and bid on projects for which they have the necessary skills and resources. Once projects are started, they may incur significant losses of money and credibility if they decide to withdraw their participation. (3)
  • Select mathematical, statistical and actuarial analysis techniques and data collection methods for their projects. They have to consider the advantages, disadvantages, costs and feasibility of each available option. For example, a statistician may select a stratified sample to survey a population. An operations researcher may select an optimization algorithm to prepare train schedules and routes and reduce transit times. An actuary may select a stochastic model to analyse stock markets and interest rates and to recommend portfolio structures. (4)
Critical Thinking
  • Judge the suitability of various table and graph types to present research findings and operational data for projects. They consider the strengths and limitations of each table and graph type for displaying particular data, messages they want to emphasize and level of technical expertise of their audiences. (2)
  • Assess the accuracy, reasonableness and completeness of data. They conduct logic checks and use their own experience to identify potential errors. For example, a demographer may assess the accuracy, reasonableness and completeness of survey data on labour force characteristics using a variety of mathematical techniques and common sense assumptions. (3)
  • May evaluate the performance of junior mathematicians, statisticians and actuaries on their project teams. As part of the assessments, they determine the extent to which juniors have achieved their various project tasks and adhered to plans, schedules and timelines. Their conclusions may lead to recommendations for further training and reassignments of the workers they supervise. (3)
  • Evaluate the completeness and clarity of policies, procedures and guidelines which they have written. They ensure that crucial information has not been omitted and that wording is not open to interpretation. For example, an actuary may evaluate the completeness and clarity of group benefit and retirement benefit plans and life, property and health insurance policies. (3)
  • May assess the quality and readiness of articles for publication in academic journals. For example, an operations researcher may be asked to review a colleague's article on an algorithm for multiple criteria optimization. The researcher evaluates the article using criteria such as the soundness of the mathematical approach, the consistency of explanations, the appropriateness of conclusions reached and the clarity of the text. (4)
Job Task Planning and Organizing

Own Job Planning and Organizing

Most mathematicians, statisticians and actuaries work in dynamic environments with conflicting demands on their time. They often work in teams, so they must integrate their own tasks and work schedules with those of many co-workers and colleagues. Their ability to work on several projects at the same time and manage priorities is critical to their jobs. Delays in getting accurate data, pressures from managers and clients and other unexpected events force them to frequently reorganize job tasks. (3)

Planning and Organizing for Others

Mathematicians, statisticians and actuaries contribute to long-term and strategic planning for their organizations. They may be responsible for assigning job tasks and creating work schedules for co-op students and junior mathematicians, statisticians and actuaries. (3)

Significant Use of Memory
  • Remember multiple security codes to access computers and networks. Large organizations force password changes at regular intervals and system operators may prohibit the ones that depend on common mnemonic devices.
  • Remember the names, specialization areas, interests and concerns of co-workers, colleagues and clients to save time, facilitate communication, develop positive relationships and build trust.
Finding Information
  • Find information about past projects by searching reports, files and archives and talking to co-workers. For example, an actuary may search archived files to find information about a pension plan developed for a client. (2)
  • May find information to support public and private sector decision making and policy development processes by reviewing literature and conducting surveys. They may design statistical samples, write questionnaires, supervise survey implementation, collect data and analyse results to find the information needed by decision makers and policy developers. (3)
  • Find information about mathematical theories and techniques used to solve specific scientific, engineering, financial, management and socioeconomic development problems by conducting extensive literature searches. They analyze and integrate information from a wide range of sources to facilitate their own mathematical research and applications. (4)
Digital technology Help - Digital technology
  • Use the Internet. For example, mathematicians, statisticians, demographers and operations researchers may access library databases to find research articles and reports. Actuaries may perform keyword searches to obtain information on insurance and pension related topics. (2)
  • Use word processing. For example, they may write, edit and format text for letters, survey questionnaires, policies, procedures, guidelines and proposals using programs such as Word. They may also write, edit and format articles and reports containing mathematical equations using text editing programs such as Notepad, TeX and LaTeX. They may supplement text with imported graphs and computations. (3)
  • Use graphics software. For example, they may create slide shows using presentation software such as PowerPoint. In order to develop effective presentations for clients, co-workers and colleagues, they may import graphs, scanned images and word processing files. They may use programs such as Visio to draw schematics and diagrams. (3)
  • Use databases. For example, mathematicians, statisticians, demographers and operations researchers may create and modify databases for their research projects using programs such as Access and MySQL. Actuaries may create and modify databases to maintain records of clients, retiree benefits and account values. They may also search, display and print data from these databases. (3)
  • Use spreadsheets. For example, mathematicians, statisticians, demographers and operations researchers may use spreadsheet programs such as Excel to create budgetary tables for grant applications, display research data and calculate probability distributions. Actuaries may create spreadsheet tables to calculate benefits for pension plan participants and incurred losses for insurance carriers. (3)
  • Use bookkeeping, billing and accounting software. For example, actuaries may use financial planning software such as FP Solutions to develop retirement plans for clients. (3)
  • Use communication software. For example, they may create and maintain distribution lists, receive correspondence and send e-mail to clients, co-workers and colleagues. They may also attach electronic files to their e-mail. (3)
  • Use other computer and software applications. For example, they may use programs such as Acrobat to convert text files to portable document formats. They may use utility programs such as WinZip to condense large electronic files before sending them as attachments to e-mail. Actuaries may also use specialized software to calculate actuarial factors. (3)
  • Use statistical analysis software. For example, statisticians and demographers may use programs such as SPSS, SAS, Stata, Statistica, MatLab and SciLab to perform statistical analyses of research data, calculate means, medians, standard deviations and confidence intervals, and perform linear regressions. They may also use these programs to draw bi-dimensional and three-dimensional graphs of mathematical functions. (4)
  • Do programming and system and software design. For example, mathematicians, statisticians, demographers and operations researchers may use software such as 'R' to program research data calculations and graphical displays. Actuaries may use software such as Visual Basic, Fortran, 'C' and APL to program actuarial reports. (5)
Additional information Help - Additional information Other Essential Skills:

Working with Others

Mathematicians, statisticians and actuaries coordinate and integrate job tasks with project teams comprising managers, coworkers and colleagues. They work closely with managers to define project priorities, methodologies and schedules and to monitor progress. They may supervise and train co-op students and junior mathematicians, statisticians and actuaries assisting them with project tasks. (3)

Continuous Learning

Continuous learning is an integral part of the job of mathematicians, statisticians and actuaries. They are expected to further their knowledge of mathematical, statistical and actuarial theories and techniques and keep abreast of legislative changes, technological advances and other events affecting their practices. On a day-to-day basis, they acquire new learning through self-study and experimentation, speaking with co-workers and colleagues, browsing the Internet and reading textbooks, e-magazines, e-bulletins, government legislation and academic journals. They also attend conferences, seminars, symposia, workshops and courses on topics relevant to their specialization. They may be required by their employers to develop their own learning plans. (4)

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