Introduction

Statistics is an area of study that provides tools for analyzing real-world problems when there is underlying variability in the collected data.

A statistical question is one that answers "yes" to both of the following:

  • Can the question be answered by collecting data?

  • Will there be variability in the data?

Statistical questions have no single, unique answer.

For example, suppose we wish to answer the following question:

\qquad How much does a typical newborn kitten weigh?

Let's go through our checklist and determine whether this is a statistical question:

  • We can answer the question by collecting data. To do this, we need to record the weights of some newborn kittens. \quad {\color{green}{\checkmark}}

  • There will be variability in the data because we expect different kittens to weigh different amounts. \quad {\color{green}{\checkmark}}

Therefore, "How much does a typical newborn kitten weigh?" is a statistical question.

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Example: Identifying Statistical Questions

Which of the following are statistical questions?

  1. How many people typically watch ABC News on a Saturday evening?
  2. How old was Abraham Lincoln when he became president of the United States of America?
  3. How tall was Miles on his 5th birthday?
  4. What is the height of a randomly selected oak tree?
EXPLANATION

Let's examine the items one by one:

  • Question I is a statistical question:

    • We can answer the question by collecting data. In this case, we need to collect data on the number of people who watch the news.

    • There is variability in the data. We expect the number of people who watch the news on Saturday evening will vary from week to week.

  • Question II is not a statistical question. There is only one answer (Abraham Lincoln was 52 when he became president), and there is no variability.

  • Question III is not a statistical question. There is only one answer, and there is no variability.

  • Question IV is a statistical question:

    • We can answer the question by collecting data. In this case, we need to collect data about the heights of oak trees.

    • There is variability in the data. The height of an oak tree varies from tree to tree.

Therefore, the correct answer is "I and IV only."

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Practice: Identifying Statistical Questions

Which of the following are statistical questions?

  1. How many days does it rain in Mexico in a typical week?
  2. How many nuts does a squirrel eat daily?
  3. How much water is needed to fill a ten-liter water bottle?
a
 I and III only
b
 I only
c
 II and III only
d
 II only
e
 I and II only
Practice: Identifying Statistical Questions

Which of the following is a statistical question?

a
 How much time do California students spend on their homework each evening?
b
 Anita likes strawberries
c
 What is Don's favorite meal?
d
 How much time did Don spend on his math homework on his eighth birthday?
e
 How many pets does Anita have?
Example: Identifying Non-Statistical Questions

Which of the following are NOT statistical questions?

  1. How many words are there in the poem "From a Railway Carriage" by Robert Louis Stevenson?
  2. How many yards are in a mile?
  3. How long does it typically take to read the novel "Charlotte's Web" by E. B. White?
EXPLANATION

Let's examine the items one by one:

  • Question I is not a statistical question. There is only one answer, and there is no variability in that answer.

  • Question II is not a statistical question. There is only one answer ( 1\, 760 yards equals one mile), and there is no variability to that answer.

  • Question III is a statistical question:

    • We can answer the question by collecting data. In this case, we should collect data from several people who have read the book.

    • There is variability in the data. The time spent reading the book will depend on each person.

Therefore, the correct answer is "I and II only."

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Practice: Identifying Non-Statistical Questions

Which of the following are NOT statistical questions?

  1. How many episodes does a typical TV series have?
  2. How old was Isaac Newton when he died?
  3. How many seasons are there in one year?
a
 II only
b
 I, II and III
c
 II and III only
d
 I and III only
e
 I only
Practice: Identifying Non-Statistical Questions

Which of the following are NOT statistical questions?

  1. How many faces does a cube have?
  2. How long does it take for a pizza restaurant to deliver a pizza?
  3. How many candies can you buy with $\$10$ in a typical store?
a
 III only
b
 I and III only
c
 II only
d
 I and II only
e
 I only
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