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Asking a question

Statistics and data · level 1, lesson 4 of 5

A question to start

A teacher wants to make a picture graph of the class's favourite pets. She asks, "What is your favourite pet?" Here are some of the answers she gets:

  • "My grandma's dog, Rex!"
  • "Fluffy ones."
  • "A dinosaur!"
  • "I like cats and dogs and also horses."
  • "Dog."
  • "Puppies!"

Try to make a picture graph from those answers. Is "Rex" the same as "dog"? Is "puppies" the same as "dog"? Where does "fluffy ones" go? Where does the child who likes three pets put a sticker?

It is very hard. The answers are all good answers, but they do not sort. In this lesson you learn how to ask a question so that the answers sort themselves, and every child's answer can be counted.

The idea

Data starts with a question

The answers people give you are called data. All the data in this level, the stickers and the counts, came from somebody asking a question. A good question gives data that you can sort and count. A muddled question gives a muddle.

Asking the same question to lots of people, and writing down their answers, is called a survey.

Give choices

The best trick is to give choices. Instead of "What is your favourite pet?", ask:

"Which of these pets do you like best: dog, cat, fish, or something else?"

Now every child picks one of four answers. The answers sort straight into four groups. "Rex" becomes "dog". "Puppies" becomes "dog". The dinosaur fan picks "something else".

Choosing good choices

Choices need care. Here is what to think about.

  1. Not too many. Three to five choices is plenty. Ten choices would give ten tiny rows, and it would be hard to see anything.
  2. Easy to tell apart. "Dog" and "puppy" should not both be choices, because a puppy is a dog. Each child should know exactly which one is theirs.
  3. A choice for everyone. What if a child's favourite is a hamster, and hamster is not on the list? Add a choice called "something else", so nobody is stuck. (Some surveys call it "other".)

Everyone answers once

A survey is fair when everyone answers exactly once. Not zero times, and not two times.

  • If someone is missed, their answer is lost, and the graph is not about the whole class.
  • If someone answers twice, their choice counts double. That is not fair to everybody else.

How can you make sure? Use a class list. Write every child's name. As each child answers, put a tick next to their name, and write down their choice.

Name Tick Choice
Ava ✓ dog
Ben ✓ cat
Cleo ✓ dog
Dev ✓ something else
Emma

Emma has no tick yet, so you know she still needs to answer. Nobody can get two ticks, because there is only one line for each name.

Ways to collect the answers

There are many ways to collect answers. Each one has a good side and a tricky side.

  • Hands up. Quick! But children may look around and copy their friends. Some may put their hand up twice, for two choices, by mistake.
  • Stand in a corner. Each corner of the room is one choice. Fun, and easy to count. But friends may follow friends.
  • A block in a cup. Each child drops one block into the cup for their choice. Nobody sees what you chose. Then you tip out each cup and count.
dog cat fish something else
  • A sticker on the graph. Each child puts their own sticker straight on a picture graph. The graph builds itself!

Whichever way you choose, one rule stays the same: one answer from each child, and every child answers.

Questions that work, and questions that do not

Some questions are not good for counting at all.

  • "Is your dog nice?" Only children with dogs can answer, and "nice" means different things to different people.
  • "How much do you like cats?" Everyone would answer in different words.

A good counting question has a short list of clear answers that everyone can choose from. "Do you have a pet at home: yes or no?" is a great question. Every child can answer, and there are just two groups.

After the survey

Once you have the answers, you know what to do from the last three lessons:

  1. Sort the answers into groups (one group for each choice).
  2. Count each group, and check that the total equals the number of children.
  3. Draw a picture graph.

With the cups above, the counts are: dog 6, cat 5, fish 1, something else 3. Total: 6 and 5 make 11, and 1 more makes 12, and 3 more makes 15. If there are 15 children in the class, everyone answered once.

Worked examples

Example 1. Fixing a muddled question. A child wants to know what the class likes to eat for a snack. She asks, "What do you like to eat?" What goes wrong, and how can she fix it?

  1. Children will say all sorts of things: "pizza", "everything", "my mom's soup", "apples and cheese".
  2. Many answers will not sort. "Everything" fits no group. "Apples and cheese" is two answers.
  3. Fix: give choices, and say "pick one". "Which snack do you like best: fruit, crackers, yogurt, or something else? Pick one."
  4. Now every answer goes in exactly one of four groups.

Example 2. Too many answers. A class of 22 children voted for a class name with hands up. The counts were: Stars 9, Rockets 8, Comets 9. Is something wrong?

  1. Find the total: 9 and 8 make 17, and 9 more make 26.
  2. But there are only 22 children. 26 is 4 too many.
  3. So some children voted twice (maybe they liked two names and put their hand up both times).
  4. The vote is not fair. Fix: vote again with a class list and ticks, or with blocks in cups, so each child votes only once.

Example 3. Planning a survey. Plan a survey to find out what the class would like to play at recess.

  1. The question: "Which game would you like to play at recess: tag, ball games, skipping, or something else? Pick one."
  2. Who answers: every child in the class, once each. Use the class list with ticks.
  3. How to collect: each child drops a block in one of four cups, so nobody copies.
  4. After: sort, count, check the total equals the number of children, and draw a picture graph.

Try it

  1. Why is "What do you like?" a hard question to make a picture graph from?
  2. Make the question "What is your favourite animal?" into a question with four choices.
  3. Why is it a good idea to have a choice called "something else"?
  4. A class has 18 children. In a vote about a trip, the counts were: zoo 7, farm 6, park 3. Add them up. What might have happened?
  5. Why might "hands up" give a different answer from "blocks in cups"?
  6. Which question is better for a survey, and why? (a) "Do you walk to school: yes or no?" (b) "How do you feel about walking?"
  7. Kai asks, "Which fruit do you like best: apple, banana, fruit, or something else?" One of his choices is a problem. Which one, and why?
  8. Plan your own survey for your family: write the question, the choices, and how you will make sure everyone answers once.
Answers
  1. People will answer in many different ways, about many different things. The answers will not sort into a few groups, so you cannot count them.
  2. One example: "Which animal do you like best: lion, horse, rabbit, or something else? Pick one." Any short list with a "something else" choice works.
  3. So that everyone has an answer to choose. Without it, a child whose favourite is not on the list is stuck, and might not answer, or might pick a choice that is not really theirs.
  4. 7 and 6 make 13, and 3 more make 16. That is 2 fewer than 18. So 2 children did not vote: maybe they were away, or they were missed. The total check found it.
  5. With hands up, children can see each other, so some may copy their friends, or vote twice. With blocks in cups, nobody sees your choice and you only have one block.
  6. (a) is better. There are only two answers, yes or no, and everyone can answer. (b) would get answers in all sorts of words that are hard to sort and count.
  7. "Fruit" is the problem. An apple is a fruit and a banana is a fruit, so a child who likes apples could pick "apple" or "fruit". Choices must not cover the same thing twice.
  8. Many answers work. For example: "Which movie night snack do you like best: popcorn, fruit, pretzels, or something else? Pick one." Write every family member's name and tick each one as they answer.

Common mistake

Asking without choices. An open question gets answers in all sorts of words that do not sort. Give a short list of clear choices, and include "something else".

Letting people answer twice, or missing someone. Then the counts are wrong, and the graph does not show the whole group. Use a list of names and tick each person once. Always check that the total equals the number of people.

Where it leads