Ten friends gave me ten different answers to my survey. What went wrong?
Your guess
Pick one before you read on. It is fine to be wrong.
By the end you can
Write a clear question for a survey
Group data into classes like 0 to 9 and 10 to 19
Tell counted data from measured data
A survey asks many people the same question. The answers you collect are called data. Good data comes from a good question.
A good survey question asks about one thing. It means the same to everyone. Its answers can be counted. Give a choice for every answer, such as "other".
"How do you go?" is too open. "Do you like it?" does not say what "it" is. "Walk, bus or other?" gives a choice for every answer, and the answers can be counted.
Ana asks 20 children how many books they read last month. The answers run from 0 to 29. A list of 20 numbers is hard to read. So we sort the numbers into groups called classes.
Draw it first
Sort 20 answers into classes
1 Write down all 20 answers. Each one is a number of books.
2 Make a box for each class. Put each answer in the box where it fits.
3 Count the answers in each box. These counts are the frequencies.
9 + 7 + 4 = 20, so every answer is in exactly one class.
Good classes are usually the same width. The classes 0 to 9 and 10 to 19 both hold 10 whole numbers. There is no gap between classes, and they never overlap. So every answer fits one class only. The last class may be open, such as "10 or more".
Worked example
Sipho asked 10 children how many books they read. The answers are 4, 13, 8, 21, 17, 2, 10, 25, 6, 19. Sort the answers into the classes 0 to 9, 10 to 19 and 20 to 29. How many are in each class?
Class 0 to 9: the answers 4, 8, 2 and 6 fit. That is 4.
Class 10 to 19: the answers 13, 17, 10 and 19 fit. That is 4.
Class 20 to 29: the answers 21 and 25 fit. That is 2.
Check: 4 + 4 + 2 = 10, the number of children asked.
Answer: The counts are 4, 4 and 2.
Sipho's 10 answers, sorted into their classes. The number under a box is how many answers it holds.
Data comes in two kinds. Counted data is found by counting, so it is a whole number: 3 books, 0 pets. Measured data is found with a ruler, a scale or a clock. It can be 142.5 cm or 7.25 s.
Ask: did I count it, or measure it? Counted data skips between whole numbers. Measured data can be any size in between.
Classes like 0 to 9 and 10 to 19 work for counted data. A measured 9.5 cm would fit neither of them. So measured classes are written like 10 cm up to 20 cm. The 20 cm goes in the next class.
See it three ways
With things
Ana asks 10 children how they get to school. She makes one mark for each answer. Every fifth mark crosses the four before it.
As a picture
In symbols
walk 6, bus 3, car 1. 6 + 3 + 1 = 10 children.
Try it
A survey at home
You need: paper and a pencil, ten people to ask, or ten answers you can find.
Write the question: "How many people live in your home?"
Ask ten people and write each answer down.
Make three classes: 1 to 3, 4 to 6 and 7 to 9. If a home has 10 people or more, add a class "10 or more".
Put each answer in its class and count.
What you will see: Every answer fits one class, and the counts add up to 10. If they do not, an answer fits no class, or a class has a gap or an overlap.
If you cannot try it, this is what happens.
A wrong idea many people have
Classes can overlap, like 0 to 10, 10 to 20 and 20 to 30.
Why it feels right: The numbers 10 and 20 look like good places to stop and start.
The test that breaks it: Put the answer 10 in the classes 0 to 10 and 10 to 20. It fits both, so you do not know which count to add it to.
What is true: Every answer must fit one class only. Use 0 to 9, then 10 to 19, then 20 to 29.
Key words
survey
asking many people the same question.
data
the facts and numbers you collect.
class
one group of values, such as 10 to 19.
counted data
data found by counting, always a whole number.
measured data
data found with a ruler, scale or clock.
Back to your guess
The answer is B: My question was not clear, so each friend answered a different question.
A survey question must mean the same thing to everyone. "How do you travel?" gets answers like "fast" and "in the morning". Give choices: walk, bus, car or another way. Then the answers can be counted.
Check yourself
Try each one before you look. A wrong answer tells you where to go next.
Tariq wants to know how children travel to school. Which is the clearest survey question?
See the answer
How do you usually get to school: walk, bicycle, bus, car or other?
It asks about one thing, it gives choices, and every answer can be counted.
If you chose B: That asks about feelings, not about travel. A question must ask about the thing you want to know. Go to M3.7.1.
If you chose C: This is too open. One child says "fast" and another says "in the morning". Those answers cannot be counted. Go to M3.7.1.
The answers in a survey run from 0 to 29. Which classes are set up correctly?
See the answer
0 to 9, 10 to 19, 20 to 29
Each class holds 10 whole numbers. One class ends at 9 and the next starts at 10. There is no gap and no overlap.
If you chose A: The answer 10 fits both 0 to 10 and 10 to 20. Classes must not overlap. Go to M3.7.1.
If you chose B: The answer 10 fits no class here. Classes must leave no gap. Go to M3.7.1.
Which of these is measured data?
See the answer
The mass of a bag of rice
You weigh the rice with a scale. A mass can be any size, such as 2.5 kg. The other two are counted.
If you chose A: You count pets: 0, 1, 2. Counted data is a whole number. Go to M3.7.1.
If you chose C: You count players one by one. That is counted data. Go to M3.7.1.
The classes are 0 to 9, 10 to 19 and 20 to 29. In which class does the answer 19 go?
See the answer
10 to 19
19 is at least 10 and at most 19, so it fits the class 10 to 19.
If you chose B: The class 0 to 9 stops at 9. The answer 19 is bigger than 9. Go to M3.7.1.
If you chose C: The class 20 to 29 starts at 20. The answer 19 is smaller than 20. Go to M3.7.1.
The boxes show the books read by 20 children. How many children read 10 to 19 books?
See the answer
7 children
The number under the box named 10 to 19 is 7.
If you chose A: 19 is the end of the class, not a count. Read the number under the box. Go to M3.7.1.
If you chose B: That is the count for the class 0 to 9. Look at the box named 10 to 19. Go to M3.7.1.
Hana asked 8 children how many books they read: 5, 12, 27, 9, 14, 3, 21, 17. How many of them read 10 to 19 books?
See the answer
3 children
The answers 12, 14 and 17 fit 10 to 19. That is 3 children.
A frequency table shows 6, 11 and 8 children in three classes. How many children were asked?
See the answer
25 children
Add the counts: 6 + 11 + 8 = 25.
Keep it
Copy this into your exercise book.
A clear survey question asks about one thing and has answers you can count. Classes have the same width, no gap and no overlap. Counted data is whole numbers. Measured data can be any size.
Draw: Draw three boxes named 0 to 9, 10 to 19 and 20 to 29. Write six answers in the right boxes.
