D. Statistical Analysis · Two-Variable Data Analysis and Validity

Careers and University Programs in Data Management

D3.3About 60 minutes

Learning goals

I can describe several occupations that use data management, including actuary, statistician, business analyst and sociologist.
I can connect the skills of this course to specific tasks in those occupations.
I can identify university programs that prepare students for data-related careers and find their admission requirements.
I can research a data-related career using reliable sources and summarize what I find.

Words to know

actuary
A professional who uses probability, statistics and financial mathematics to measure and manage risk, especially in insurance and pensions.

statistician
A professional who designs studies and surveys, analyses data and draws conclusions with measured uncertainty.

business analyst
A professional who uses data to understand how an organization works and to recommend improvements.

sociologist
A social scientist who studies groups, communities and societies, often using surveys and statistical analysis.

data scientist
A professional who combines statistics, programming and subject knowledge to find patterns and build models from large data sets.

professional designation
A title earned by meeting the education, exam and experience requirements of a professional body, such as FCIA for actuaries.

Who gets paid to think like this?

In this unit you calculated correlations, fitted models, hunted for outliers and lurking variables, and judged claims in the media. These are not just school skills. Insurance companies, hospitals, governments, sports teams, banks, tech companies and research labs hire people to do exactly this, every day.

The curriculum asks you to gather and interpret information about occupations that use data management, such as actuary, statistician, business analyst and sociologist, and about the university programs that lead to them.

Each line links a skill you have practised in MDM4U to a career that relies on it. Every career on the right uses several of the skills.

Four careers named in the curriculum

Actuary. Actuaries estimate the cost of future uncertain events, such as car accidents, house fires, illness or how long people will live, and use those estimates to set insurance premiums and plan pensions. They use expected value (from Discrete Probability Distributions), probability models and financial mathematics. In Canada, the professional body is the Canadian Institute of Actuaries, and the full designation is FCIA (Fellow of the Canadian Institute of Actuaries). Actuaries pass a series of professional exams, usually while studying and working.

Statistician. Statisticians design surveys and experiments, choose samples, analyse data and report results with their uncertainty. They work for agencies such as Statistics Canada, for hospitals and drug companies (clinical trials), for polling firms, and in universities. The Statistical Society of Canada offers professional accreditation (A.Stat. and P.Stat.).

Business analyst. Business analysts use data from sales, customers and operations to find problems and recommend changes: which products to stock, how to schedule staff, whether a new process saves money. Regression, dashboards and clear communication are central.

Sociologist. Sociologists study how groups and societies work: families, education, work, inequality, communities. Much of their evidence comes from surveys and contingency tables (such as Statistics Canada tables of income or unpaid work by gender), and they must think carefully about bias, sampling and causation.

Others include data scientists, epidemiologists (who track diseases in populations), economists, market researchers, psychologists, environmental scientists, sports analysts, quality-control engineers and pollsters.

Worked example

Example 1: An actuary's first estimate

An insurer's records show that each year about 2% of the policies of one type have a claim, and the average claim is $6500. Estimate the expected claim cost per policy per year. Why must the premium be higher than this?

Expected cost = P(claim) × average claim = 0.02 × $6500 = $130.
This is an expected value: across thousands of policies, the average cost per policy should be close to $130.
The premium must also cover the company's expenses (staff, buildings, commissions), a margin for uncertainty (a bad year with more claims), and profit.

About $130 per policy per year in expected claims, so the premium will be somewhat higher. Real actuaries refine this with many variables (age, location, driving record) and regression models.

Worked example

Example 2: A business analyst's regression

A chain of 12 stores finds that weekly sales (y, $1000s) and weekly hours of staff on the floor (x) have r = 0.82 and ŷ = 0.35x + 18. A manager wants to add 20 staff hours to every store. What can the analyst say?

Slope: each extra staff hour is associated with about $350 more weekly sales (0.35 thousand dollars).
20 more hours: predicted increase 20 × 0.35 = 7, about $7000 per week per store, if the relationship were causal.
Caution: busier stores may simply schedule more staff (reverse cause). The data are observational.
Recommendation: run a small experiment, randomly choosing some stores to get extra hours for a few weeks, and compare with the others.

The model suggests a possible gain of about $7000 per store per week, but the analyst should recommend a randomized trial before spending on all 12 stores, because the correlation may not be causal.

Worked example

Example 3: A sociologist's table

In a survey of 800 young adults, 60% of those who grew up in cities and 45% of those who grew up in rural areas finished a post-secondary program. 500 grew up in cities. How many in each group finished, and what would a sociologist investigate next?

Cities: 0.60 × 500 = 300 finished. Rural: 800 − 500 = 300 people, and 0.45 × 300 = 135 finished.
The conditional percentages differ (60% vs 45%), so growing up in a city or rural area is associated with finishing post-secondary.
Possible lurking variables: distance to a college or university, cost of moving away, family income, local job opportunities.

300 and 135. A sociologist would look at these lurking variables (for example, by stratifying by distance to the nearest campus) before drawing conclusions about causes, and would think about policy options such as distance learning or relocation support.

A typical route to the actuarial profession. Each university sets its own admission requirements, so check the programs you are interested in.

University programs and admission

Programs that lead to these careers include statistics, actuarial science, mathematics, data science, computer science, economics, commerce or business (especially analytics), sociology, psychology, health sciences and environmental science. Several Ontario universities, including the University of Waterloo and the University of Toronto, offer actuarial science programs; many offer statistics and data science.

MDM4U is a required or recommended course for many university programs, especially in business, the social sciences and the health sciences, while math-intensive programs often also require Advanced Functions (MHF4U) and Calculus and Vectors (MCV4U). Requirements change and differ by program, so always check the university's admission pages or the Ontario Universities' Info website. Co-op programs let you alternate study terms with paid work terms, which is a common way to try out careers such as data analyst or actuarial assistant.

Finding reliable career information

Job Bank (Government of Canada) has job descriptions, typical wages and outlooks by province.
Professional bodies: the Canadian Institute of Actuaries, the Statistical Society of Canada, and others describe their professions and designations.
University program pages list admission requirements and courses.
People: an informational interview with someone in the job (with a parent's help to arrange it) is one of the best sources of all.

Apply the skills of this unit: who wrote it, when, and do they have something to sell?

Just for fun

Why are actuaries never surprised at their birthday parties? They calculated the probability of a party weeks ago, and adjusted the premium on the cake.

Hands-on activity

Career research profile

You need: a computer or phone with internet access, and paper.

Choose one of the careers in this lesson (or another data-heavy career that interests you, such as sports analyst or epidemiologist).
Using at least two reliable sources (for example, Job Bank and a professional body or university site), find: what the job involves day to day, the education and any designation needed, typical employers in Ontario, and the job outlook.
Find two university programs in Ontario that could lead to this career and write down their admission requirements (which Grade 12 courses?).
List three skills from this course the job uses, with a specific example of each.
If you can, interview someone who works with data (a relative, a family friend, someone from a local business) for 10 minutes. Ask what a typical week looks like and what they wish they had learned in high school.
Summarize everything on one page.

What to look for: a strong profile names its sources, gives specific examples ("actuaries calculate expected claim costs"), and notes anything uncertain or that varies between employers.

Your turn

Name the four occupations the Ontario curriculum gives as examples of careers that use data management.

Which career is most closely linked to setting insurance premiums?

A professional designs a national survey, chooses the sample and reports the margin of error. What is the occupation?

Which MDM4U topic would a sociologist use to compare post-secondary completion rates for two groups?

An insurer estimates a 0.5% chance of a claim per year, with an average claim of $40 000. Find the expected claim cost per policy.

Why should you check university admission requirements yourself rather than rely on a friend's advice?

Give one reason a business analyst should be careful about using a regression model to justify spending money.

More practice: warm-up

What does FCIA stand for?

Name Canada's national statistical agency.

Name a Government of Canada website with job outlooks.

Which professional body offers the P.Stat. designation?

Name two university programs that lead to data-related careers.

More practice: on your own

A sports analyst finds r = 0.7 between a hockey team's shots on goal per game and goals per game over a season. What would they report to the coach, and what caution would they add?

An epidemiologist sees that flu cases and hot chocolate sales rise together each winter. How would they explain this to a reporter?

A market researcher surveys 400 customers who signed up for the company's newsletter and finds 90% like a new product. What bias should they mention?

Explain how a data scientist's work uses both residual plots and the idea of extrapolation.

A Grade 12 student wants to become an actuary. Suggest three concrete steps they could take in the next year.

Challenge

An insurer sells 10 000 policies. Each has a 2% chance of a $6500 claim (independently). Find the expected number of claims and the expected total cost. Why does selling many policies make the insurer's total cost more predictable?

Write a short paragraph (4 to 5 sentences) explaining to a Grade 10 student why the skills in this unit matter for careers even outside mathematics.

Choose a news story that uses data. Identify which occupation probably produced the original data and which might have analysed it, and explain the role of each.

Check your understanding

Quiz

Which occupation is most closely associated with calculating the risk and cost of future events for insurance?

Which skill from this course does an actuary use when finding P(claim) × average claim?

A professional who designs a national survey and reports a margin of error is most likely a:

Which is the most reliable way to find the admission requirements of a university program?

A business analyst finds sales and staff hours are correlated (r = 0.82). What should they recommend before adding staff everywhere?

Which Canadian organization grants the FCIA designation?

For parents and teachers

Big idea (D3.3): data management skills lead directly to careers such as actuary, statistician, business analyst, sociologist, data scientist and epidemiologist, and to university programs in statistics, actuarial science, data science, economics, business and the social and health sciences.

How to help: This is a great lesson for family conversation. If you or someone you know uses data at work, share an example. Help your teen arrange a short informational interview, and look at university admission pages together; requirements vary, so check official sources.

Common difficulties:

Thinking data careers are only for people who want to do "pure math".
Relying on hearsay for admission requirements.
Copying job descriptions without connecting them to specific skills from the course.