"Risk" is the chance of loss or harm. Personal financial risk exists when unexpected events can damage health, income, property wealth or future opportunities. Insurance is a product that allows people to pay a fee, called a premium, upfront to transfer the costs of a potential loss to a third party. Insurance companies analyze the outcomes of individuals who face similar types of risks to create insurance contracts (policies). By collecting a relatively small amount of money, called a premium, from each policyholder on a regular basis, the company creates a pool of funds to compensate those individuals who experience a large loss. Insurance companies charge high premiums to cover high-risk individuals and events because the risk of monetary loss is greater for these individuals and events. People can lower insurance premiums by behaving in ways that show they pose a lower risk and by assuming higher deductibles. A deductible is a fixed amount an insured person must pay per loss before the insurance company will pay a claim. Auto insurance is a type of property insurance that pays for damage or loss to the insured’s car and often includes liability coverage for actions of the insured which cause harm to other people or their property. Insurance companies consider a number of factors when determining the level of risk associated with providing car insurance to various groups of people. In this lesson, students examine age, gender and driving record using two-way tables.
A two-way table is a tool used to organize data from two categorical variables. A categorical variable is a variable that can take on one of a limited and usually fixed number of possible values. Two-way tables often summarize large amounts of information comparing two sets of data organized in rows and columns.
Once students have the data, marginal and conditional distributions can be computed and used to compare risk levels for those seeking insurance. The marginal distribution of one of the categorical variables in a two-way table is the distribution of values of that variable among all individuals described by the table. A conditional distribution of a variable is the distribution of values of that variable among only individuals who have a given value of the other variable. There is a separate conditional distribution for each value of the other variable (faculty.etsu.edu/gardnerr/1530/chapter6.pdf). A teenage male is a high risk for auto insurance companies (an example of marginal distribution). However, of those male teenager drivers, those who take a driver safety class are a lower risk (an example of conditional distribution). Students will use a two-way table and marginal and conditional distributions to determine which group or groups are a higher risk for auto insurance companies and therefore will be charged higher premiums and deductibles.
Note to teachers: the term marginal in this lesson is used differently from the customary use of the term in economics. In economics, marginal refers to the additional or extra of something, such as the additional or marginal cost of production.