Learning Goals
- Distinguish between questions that have exact answers and those that don’t.
- Identify questions that anticipate variability.
In the What to Know assignment and in the following Forming Connections, you will need to understand some key vocabulary terms and associated ideas. In particular, you will need to distinguish between questions that have exact answers and those that don’t, and you will need to know when a question anticipates variability in the data.
Driving Variation
In the next in-class activity, we will be working on writing good statistical questions, and we will be considering statistical questions in the context of drivers in the United States. In this setting, you’ll encounter some questions about driving in the U.S. for which you’ll need to identify whether the question has an exact answer or one that could vary from person to person asked. As you work through the activity, give yourself a good opportunity to learn how to tell if a question anticipates a variety of answers by carefully reading the text and examples, then answering the questions in pairs or small groups.
Statistical Questions
Two key qualities of a good statistical question are:
- There is not an exact answer.
- The question anticipates variability.
When a question has an exact answer, it means that there is one specific answer to the question and only one clear way in which the question can be answered. This answer could be a number, “yes” or “no,” or another word or phrase, but this answer is the only possible answer.
For example, the question “Which states have a state-wide, hands-free cell phone law for drivers?” has an exact answer. Each state either does or does not have a hands-free cell phone law, so the answer to the question would be the list of states that have such a law.
However, the question “Do states with state-wide, hands-free cell phone laws tend to have fewer automobile accidents?” does not have an exact answer. To answer this question, we would need to collect data about all the U.S. states, and we would need to make some decisions about how to compare the number of accidents. For example, would we want to compare the raw numbers of accidents, or should we use some sort of proportion that takes the state’s population or typical number of drivers into account?
See the example below for a demonstration of how to identify whether a question will take an exact answer or not.
Example
Does the question “Which states have roads with speed limits over 70 miles per hour?” have an exact answer?
How about the question “Do states with higher speed limits tend to have more accidents?” Does it have an exact answer?
Hopefully you are beginning to feel comfortable interpreting what it means to say a question has an exact answer or it doesn’t. Test your understanding by working with a partner to answer Question 1.
Question 1
Which of the following questions does not have an exact answer? Select all that apply. There may be more than one correct answer.
- a) Which states typically have the most drivers on the road?
- b) Which state has the longest state highway?
- c) Do all states have the same speed limit for school zones?
- d) What percentage of states has roads with a speed limit over 70?
- e) Which state has the worst speeders?
