what you’ll need to know:
In this support activity you’ll become familiar with the following:
- 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?
Variability
The question “Do states with state-wide, hands-free cell phone laws tend to have fewer automobile accidents?” anticipates variability. To vary means to differ, and we expect the different U.S. states to have different numbers of accidents. We also expect the number of accidents to differ among states that all have a hands-free cell phone law. We anticipate that there might be a difference in the number of accidents in states with such laws compared to the number of accidents in states without those laws, and our hope in answering the question would be to use statistics to determine whether there is a pattern or some kind of general trend that describes this difference, or this variation.
Note that in order for a question to anticipate variability, the answer to the question must involve multiple data points so that there is a possibility for the data to vary.
Example
What does it mean for a question to anticipate variability? Choose the best answer from the choices below.
a) The question may be answered incorrectly depending on who is being asked.
b) The answer may vary dependent upon when the question is being asked.
c) The question must involve multiple data points so that there is a possibility for the data to vary.
Questions that anticipate variability often include words and phrases that signal patterns or tendencies that could be revealed using the methods of statistics. Work in a small group to answer the remaining two questions.
Question 2
Which of the following questions anticipate variability? Select all that apply. There may be more than one correct answer.
- a) Do states with more public transportation options tend to have less traffic?
- b) Which states typically have the highest speed limits?
- c) What percentage of registered vehicles in New York are motorcycles?
- d) Do states with more rural areas tend to have more people who drive trucks?
- e) How many highways are there in the U.S. interstate highway system?
Now you try putting it all together to identify which questions are good, statistical questions by completing the table in Question 3.
Question 3
A statistical question has both qualities we’ve discussed, so it anticipates variability in the data and it does not have an exact answer.
For example, consider the question “Which state gave the most speeding tickets in 2019?” This question anticipates variability in that we would need to check the number of tickets given by each state, and those values would most certainly vary. However, once we had the list of ticket numbers from 2019, we would just identify the largest number. Therefore, the question has an exact answer, so it is still not a statistical question.
For each of the following questions, decide if the question anticipates variability and whether it has an exact answer. Based on those facts, decide if the question is a statistical question.
| Question | Does it have an exact answer? | Does it anticipate variability? | Is it a statistical question? |
| Do highways or roads that are not highways tend to see more traffic? | |||
| How many automobile accidents in the United States were attributed to distracted drivers in 2020? | |||
| Do younger people tend to get more speeding tickets than older people? | |||
| What percentage of states allows right turns on red lights? | |||
| Which state has the most registered vehicles? | |||
| Are people who live in Southern states more likely to drive SUVs? |
You’ve had practice in this activity determining whether a question has an exact answer and anticipates variability or not. Hopefully, you feel more comfortable identifying the characteristics of a good statistical question now. It’s time to move on to the What to Know page to extend your understanding.
