What is a Statistical Question?

What is a Statistical Question? exercise

• What are the features that make a question statistical?

  Hints

  Statistical questions do not have one specific answer.

  We often would need to collect and analyse data to answer a statistical question.

  Solution

  When asking a statistical question we would expect a variety of responses. The answers are not fixed or based on facts. To answer a statistical question we would have to collect data and analyse the results.

• Are the following questions statistical or non-statistical?

  Hints

  Does the question have a fixed answer that would be the same no matter who was asked? If so, then it is not a statistical question.

  Can you collect data based on peoples answers? If so, then it is a statistical question.

  Solution

  Statistical questions include:

  How many books do 11 year olds read?

  • This would require us to gather the responses from many 11 year olds, and analyse the results.

  What is the most popular food on the lunch menu at your school?

  • The answer would vary depending on the school, and as above we would have to gather lots of data from different schools.

  What is the daily average rainfall in mm in the Michigan in June?

  • This answer would vary each year, and could also vary across the state of Michigan. To get an accurate answer, we would have to measure the rainfall each day in June over several years, and in different parts of the state.

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  Non-statistical questions are:

  • How many sides does a square have?

  • In which continent is Singapore located?

  • What is 10 x 7?

  The above questions all have a definite correct answer, and there would be no variation in the responses.

• Is the following question statistical or non statistical, and why?

  Hints

  Would different people give different answers?

  Does the answer need some kind of data collection?

  There are two correct statements to tick.

  Solution

  Correct statements are:

  This question is non-statistical

  This question has a definite correct answer.

  This is a trickier one, but it is not a statistical question. The correct answer is 4 or 5 Tuesdays, depending on which day of the week 1st June falls on. Everybody asked should say the same thing, so there would be no variety in responses.

• Is the following question statistical or non-statistical, and why?

  Hints

  There will be lots of different responses to this question.

  We could collect data from pupils in our school to answer the question.

  There are two correct statements to tick.

  Solution

  The correct statements are:

  This question is statistical.

  This question allows for data collection of teenagers' responses.

  This is a statistical question. There will be lots of different music preferences, and we can collect and analyse the data to discover the most popular genres.

• What makes a question a statistical question?

  Hints

  Remember, a statistical question doesn't have one definitive answer, but a variety of answers are expected. You cannot search the internet for an answer, since it will depend on individual circumstances.

  The answer requires data to be collected and analysed.

  Where is the world's tallest building?

  Here is an example of a non-statistical question, as there is a definite answer to this question. No data collection would be needed.

  Solution

  The correct answers are:

  A variety of answers is expected

  The answer requires data to be gathered and analysed.

  If an answer is fixed or definite, then it isn't a statistical question since every person who answers would give say the same thing. This would also mean there would be no data to analyse.

• How can we alter the following question to make it statistical?

  Hints

  We want the question to generate a range of responses, so choose a question that will have variety in answers.

  To be able to analyse the results, the question shouldn't be vague. "Fit and healthy" can mean different things to different people, so how can we analyse their responses?

  The question should be written clearly so that although we're expecting different answers, they should be given in the same format.

  Solution

  The most suitable question would be:

  On average, how many hours of exercise do pupils in our school do each week?

  In order to answer this question, you would need to collect data from pupils. Their range of responses could be grouped by number of hours, and we can then draw conclusions from the data.

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  Are pupils in your school fit and healthy?

  This is a vague question. "Fit and healthy" could mean different things to different people, so the responses would not be consistent.

  How much exercise do people in your town do each week?

  Whilst this appears to be a good question, it doesn't specify a format for the answer. Some people might answer "a lot" or "not much", and others might answer in hours, or some people could say "3 times a week". This would make the data difficult to analyse.*

  Do pupils in your class like to take part in sports or exercise?

  Again, quite a vague question. When we collect the data, we're likely to get "yes" or "no" responses, so we wouldn't get a huge amount of information from their answers. Asking which sports are most popular could allow for more variation in results.