How do you know if a question is statistical or not?

A statistical question is one for which you don't expect to get a single answer. Instead, you expect to get a variety of different answers, and you are interested in the distribution and tendency of those answers.

For example, "How tall are you?" is not a statistical question. But "How tall are the students in your school?" is a statistical question.

Central Tendency

When the answers to a statistical question are numerical data, we can ask about the central tendency of that data. For example, we might want to know, roughly, "how tall are most people in your school?"

However, this is not a precise question. There are ways of measuring of central tendency using a single number: you can find the mean (or average), the median, or the mode of the data.

Variation

Suppose you know that the average height of a student in a school is 5 feet. You may still be interested in the spread of the data. Is everyone nearly 5 feet tall, say within 2 inches? Or are there also very short and very tall people in the school?

The simplest measure of the variation is the range , calculated by subtracting the lowest value from the highest. More complex measures of variation include the interquartile range and the standard deviation or variance .

Below is a graph of two data sets, showing the number of students in two schools that got a particular score on a 10 -problem quiz.

Both data sets have the same range ( 10 ), the same mean (a little more than 6 ), and the same total number of students (you can't tell this easily from the graph, but it's true.) However, the heights of the blue blocks vary considerably compared to that of red blocks.

6.SP.1 Statistical Vs. Non-Statistical Questions < The following table gives some examples of statistical questions and non-statistical questions. Scroll down the page for more examples and solutions.

A statistical question is a question that should have different answers.

How to recognize a statistical question?

• A question is not a statistical question if it has an exact answer. For example “How old are you?”
• A question is a statistical question if the answer is a percent, range, or an average. For example “How old are the students in this room”

Examples:

1. Identify which questions are statistical and which questions are not statistical.
   • What is the favorite menu item for customers in the local restaurant?
   • What time do most people eat their lunches?
   • What did my dad eat for lunch today?
   • What do 7th graders prefer to eat for lunch?

2. In a survey about practice time per week for high school athletes, 22% practice 1 hour, 40% practice 2 hours, 25% practice 3 hours, 10% practice 4 hours and 3% practice more than 4 hours.
   Which one question is the most likely to have produced these results?
   • What is the average practice time per week required by your sport?
   • How much time do you spend doing homework during the week?
   • Is practice time longer on Mondays than Tuesdays?
   • Which sport practices the most?

3. Jessica conducted a survey using a representative sample of 50 customers from three local landscaping businesses in town. She found that 30% purchased maple trees, 24% purchased dogwoods, 20% purchased oaks, 16% purchased pines and 10% chose other types of trees.
   Which statements about the survey that Jessica conducted are most likely to be true? Select all that apply.
   • Jessica surveyed only the customers who purchased a tree.
   • Jessica asked customers what type of tree they purchased.
   • Jessica asked customers what type of plants they have in their yards.
   • The sample consists of 50 customers from three local landscaping businesses in town.
   • The population Jessica wants to know about consists of any customer of any landscaping business.

What Is A Statistical Question?

Definition: A statistical question has answers that will probably vary. Usually a statistical question will ask about a population of multiple people, events or things.

Examples Of Statistical Questions

• What time did the students in this class get up this morning?
• How many votes did the winning candidate for the Presidents of the Student Body receive in each of the past 20 years?
• What were the high temperatures in all of the Latin American capitals today?

Examples Of Non-Statistical Questions

• What time did I get up this morning?
• How many votes did the winning candidate for the Student Body receive this year?
• What was the high temperature in Mexico City today?

Statistical And Non-Statistical Questions

Examples:
Which of the following are statistical questions?

• How old are the people who have watched this video in 2013?
• Do dogs run faster than cats?
• Do wolves weigh more than dogs?
• Does your dog weigh more than that wolf?
• Does it rain more in Seattle than Singapore?
• What was the difference in rainfall between Singapore and Seattle in 2013?
• In general, will I use less gas driving at 55 mph than 70 mph?
• Do English professors get paid less than math professors?
• Does the most highly paid English professor at Harvard get paid more that the most highly paid math professor in MIT?

Statistical Questions - Common Core Standard

Students must know variability refers to the spread of data.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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