Exercises: Define Appropriate Quantities for the Purpose of Descriptive Modeling
Work through each section in order. For explanation problems, write in complete sentences. There is often more than one defensible answer — focus on justifying your choice clearly.
Recall / Warm-Up
Which of the following is an attribute rather than a measurable quantity?
38,000 fatalities per year
highway safety
$47,000 per-capita income
15 fatalities per 100 million vehicle-miles traveled
A project requires 40 person-hours of labor. Which scenario also equals 40 person-hours?
1 person working 40 hours, OR 4 people each working 10 hours
Only 40 people each working 1 hour
Only 1 person working 40 hours
4 people working 40 hours each
A city has a total annual income of $10 billion and a population of 500,000 people. What is the per-capita income? State the number, the unit, and one thing this quantity does NOT tell you about the city's residents.
Fluency Practice
Quantification means selecting or designing a specific measurable expression of an attribute. Which sentence best describes what makes a quantity choice a modeling decision?
A quantity choice is a discovery — the correct quantity is already determined by the situation.
A quantity choice is a decision made for a purpose — different quantities can legitimately measure the same attribute while telling different stories.
A quantity choice is arbitrary — any number with a unit will do.
A quantity choice is permanent — once chosen, it cannot be revised.
U.S. highway fatalities: in 2019, total fatalities were about 36,000 and total vehicle-miles traveled were about 3.3 trillion. In 2000, total fatalities were about 41,000 and vehicle-miles were about 2.75 trillion. Which statement correctly compares safety across the two years?
Highways became safer because total fatalities fell from 41,000 to 36,000.
Highways became less safe because more miles were driven in 2019.
Highways became safer: fatalities per 100 million vehicle-miles fell from 1.49 to 1.09, controlling for total driving volume.
We cannot determine safety trends from this data alone.
A town of 10 people has 9 residents earning $30,000 each and 1 resident earning $1,000,000. What is the per-capita income, and what does this illustrate?
Per-capita income = $127,000. This is a reliable picture of what a typical resident earns.
Per-capita income = $127,000. This illustrates that per-capita income is not the same as "typical" or "median" income — the one high earner pulls the average far above what 9 of 10 residents earn.
Per-capita income = $30,000. Per-capita means the most common value.
Per-capita income cannot be computed here because income is unequal.
A construction crew of 6 workers completes a project over 8 days, working 10 hours per day. How many total person-hours of labor did the project require?
A scientist observes that a liquid in a wide, shallow dish evaporates faster than the same volume in a narrow, tall container. She wants to measure "evaporation exposure." Propose a quantity for this attribute, state its units, and explain why your quantity scales correctly: if the surface area doubles, what happens to your measure?
You're viewing 2 of 6 sections.
Create a free account to continue the full exercise set and save your progress.
Create free account