D. Data · Data and ProbabilityQualitative and Quantitative Data
D1.1 A1About 40 minutes
Learning goals- I can explain the difference between qualitative and quantitative data.
- I can sort data as qualitative or quantitative.
- I can tell when a number is only a label, like a jersey number.
- I can choose which kind of data fits a question or a situation.
Words to know
data
Facts or information we collect, like answers to a survey or measurements.
qualitative data
Data that describes a quality using words or categories, like favourite season or kind of tree.
quantitative data
Data made of numbers that come from counting or measuring, like number of pets or height in centimetres.
category
A group or kind that an answer fits into, like "sledding" or "skating".
label number
A number used as a name, like a jersey number or a bus route number. It does not count or measure anything.
Remember from Grade 3
In Grade 3 you collected data in interviews, observations and experiments, and you saw two kinds of data: answers in words and answers in numbers. This year you will explain how the two kinds are different and decide when each kind is the best one to collect.
Two questions about a snow day
After the first big snowfall, Maya asks her class two questions.
Question 1: "What is your favourite thing to do in the snow?" Answers: sledding, skating, building a fort, sledding, skiing...
Question 2: "How many minutes did you play outside yesterday?" Answers: 30, 45, 60, 20, 45...
Both questions give Maya data. But the answers are very different. The first answers are words. The second answers are numbers she could add, compare and put in order. These are the two kinds of data.
Sledding and skating are answers in words: qualitative data. How many minutes the children play outside would be quantitative data. AI-generated imageQualitative data: words and kinds
Qualitative data describes a quality: what kind, which one, what colour, yes or no. The answers are words or categories.
- favourite season: winter, summer
- kind of tree in the schoolyard: maple, spruce, birch
- how you get to school: walk, bus, car
Memory trick: qualitative and quality both start with qual.
Quantitative data: counting and measuring
Quantitative data is made of numbers that come from counting or measuring. It tells how many, how much, how long or how far.
- number of pets: 0, 1, 3
- height of a bean plant: 12 cm, 15 cm
- time to run around the gym: 48 seconds
Memory trick: quantitative and quantity (an amount) both start with quant.
| Survey question | Sample answers | Kind of data |
|---|
| What is your favourite season? | winter, fall, summer | Qualitative |
| How many pets do you have? | 0, 2, 1 | Quantitative |
| What colour is your toque? | red, black, green | Qualitative |
| How tall is your bean plant? | 12 cm, 15 cm | Quantitative |
| How do you get to school? | walk, bus, car | Qualitative |
| How long can you hold a plank? | 25 s, 40 s | Quantitative |
Watch out: numbers that are names
Some numbers are only labels. They name something. They do not count or measure anything.
- the number on a hockey sweater: 88
- a bus route: Route 12
- a classroom: Room 14
If you collect everyone's favourite jersey number, the data is qualitative, even though you wrote numbers. Here is a test: Does it make sense to add these numbers or find a typical amount? If not, they are labels.
Careful: counting answers does not change the kind of data
When you count how many people chose each answer (like 12 chose sledding), the 12 is a frequency. The answers themselves (sledding, skating) are still qualitative. So a survey about favourite activities collects qualitative data, even when we count the votes.
Worked exampleExample 1: Sort the data
Is each data set qualitative or quantitative?
- the kinds of trees in the park
- the mass of pumpkins at a farm stand, in kilograms
- the number of library books each student borrowed
- the house numbers on your street
- Kinds of trees (maple, spruce, birch) are categories, so they are qualitative.
- Mass in kilograms is measured, so it is quantitative.
- Number of books is counted, so it is quantitative.
- House numbers name the houses. Adding 24 + 26 tells us nothing. They are labels, so the data is qualitative.
1 qualitative, 2 quantitative, 3 quantitative, 4 qualitative.
Worked exampleExample 2: One topic, two kinds of questions
Write one qualitative question and one quantitative question about hockey.
- Qualitative asks what kind or which one: "Which position do you like to play?" Answers: forward, defence, goalie.
- Quantitative asks how many or how much: "How many goals did you score this season?" Answers: 0, 4, 11...
Same topic, two different kinds of data. The question you ask decides the kind of data you get.
When do we use each kind?
- Use qualitative data when you want to know what kind, which one or what people prefer. Example: the class is choosing a read-aloud book, so ask which kind of book people like best.
- Use quantitative data when you want to know how many, how much or how long, or when you want to compare amounts or find a typical amount. Example: the coach wants to know how fast each runner is, so time them in seconds.
- Many projects use both. To plan a hot chocolate stand, you might ask which toppings people want (qualitative) and how many cups each person will buy (quantitative).
Worked exampleExample 3: Which kind fits the situation?
The student council wants to plan a winter carnival.
- They want to know whether students would rather have it on a Friday or a Monday.
- They want to know how many cups of hot chocolate to make.
- Situation 1 is a choice between two days. The answers are categories, so they need qualitative data. Question: "Which day do you prefer, Friday or Monday?"
- Situation 2 is about an amount. They need quantitative data. Question: "How many cups of hot chocolate will you drink at the carnival?" Then they can add up the answers.
1 needs qualitative data. 2 needs quantitative data.
Math talk
When you sort data, say why: "It's quantitative because it was measured in centimetres." If a partner sorts something differently, don't just say "you're wrong". Ask, "How did you decide?" Sometimes you will both learn something, like the idea that jersey numbers are labels.
Just for fun"My dog is fluffy." Qualitative.
"My dog chewed 3 socks this week." Quantitative... and a little worrying!
Hands-on activityData hunt at home
You need: paper, a pencil, and a ruler or measuring tape.
- Fold your paper in half. Write Qualitative on one side and Quantitative on the other.
- Walk around your home and find 5 qualitative data, like the colour of the front door, the kinds of fruit in the fruit bowl, or the type of each coat on the hooks.
- Find 5 quantitative data, like the number of chairs at the table, the length of your bed in centimetres, or the number of spoons in the drawer.
- Look for a label number too, like an apartment number or a channel number on the TV. Which side does it go on? (Qualitative!)
- Write one question of each kind to ask your family, like "What is your favourite breakfast?" and "How many minutes do you take to get ready in the morning?" Ask them and record the answers.
Math talk: "Which kind of data would help us decide what to make for breakfast on Saturday? Which kind would tell us how long to set the alarm for?"
Your turn
1"What is your favourite pizza topping?" Qualitative or quantitative?
Qualitative. The answers are kinds of toppings (words).
2"How many cousins do you have?" Qualitative or quantitative?
Quantitative. The answers come from counting.
3The length of a garter snake, in centimetres.
Quantitative. It is measured.
4The colours of the cars in a parking lot.
Qualitative. Colours are categories.
5The numbers on players' hockey sweaters.
Qualitative. The numbers are labels. They name players, they don't count or measure.
6Write a quantitative question about snow.
Sample: "How many centimetres of snow fell today?" or "How many snowballs can you make in 1 minute?" Any question whose answers are counted or measured numbers is correct.
7The librarian wants to know which kind of book students like most: mystery, comics, animals or sports. Which kind of data does she need?
Qualitative. She is asking about kinds of books.
More practice: warm-up
1"Do you like pancakes?" (yes or no)
Qualitative. Yes and no are categories.
2The temperature outside each morning.
Quantitative. It is measured in degrees.
3The number of letters in your first name.
Quantitative. You count the letters.
4The kinds of birds at a bird feeder.
Qualitative. Kinds of birds are categories.
5The mass of apples, in grams.
Quantitative. Mass is measured.
More practice: on your own
1Change this qualitative question into a quantitative question on the same topic: "What is your favourite sport?"
Sample: "How many hours a week do you play sports?" The answers are now numbers that are counted or measured.
2Change this quantitative question into a qualitative one: "How many minutes do you read each night?"
Sample: "What kind of books do you like to read?" or "Where do you like to read?" The answers are now words.
3Sam's survey results say: "12 people chose skating and 8 chose skiing." Sam says, "Those are numbers, so my data is quantitative." Is he right?
No. The answers people gave (skating, skiing) are qualitative. The 12 and 8 are frequencies: they count how many people gave each answer.
4Does it make sense to find a typical amount for the bus route numbers 5, 12 and 31? Why?
No. Route numbers are labels. A "typical" route number like 16 would mean nothing. Route numbers are qualitative data.
5The class is ordering pizza for a party. Which kind of data helps them decide how many pizzas to order? Write the question.
Quantitative data. Sample question: "How many slices will you eat?" Add all the answers to find the total number of slices.
Challenge
1Plan a mini project about your family's breakfasts. Write one qualitative question and one quantitative question. Say what each one would tell you.
Sample: Qualitative: "What is your favourite breakfast?" tells you what to make on a special morning. Quantitative: "How many minutes do you take to eat breakfast?" tells you how much time to plan. Any pair where one has word answers and one has counted or measured answers is correct.
2A garden club wrote down how tall their sunflowers were: "tall, short, 142 cm, medium, 96 cm". What is the problem? How could they fix it?
Some answers are qualitative (tall, short, medium) and some are quantitative (142 cm, 96 cm), so they can't be compared fairly. Fix: measure every sunflower in centimetres. Then they can put them in order and find the tallest. ("Tall" might mean something different to each person.)
3Describe a situation where you would need both kinds of data.
Sample: The school store wants to know which snacks students like (qualitative) and how many of each snack it sells each day (quantitative), so it knows what to buy and how much. Any situation that uses a "which kind" question and a "how many/how much" question is correct.
Quiz
1. Which data is quantitative?
2. Which data is qualitative?
3. The numbers on hockey sweaters are...
4. The word quantity means...
5. A coach wants to know how far each student can throw a ball. What kind of data does she need?
6. Which question collects qualitative data?
What this lesson teaches: the difference between qualitative data (words or categories: favourite season, kind of pet) and quantitative data (numbers from counting or measuring: number of pets, height in cm), and when each kind is useful (D1.1). Talking about thinking and listening to others (A1) is built in.
How to help at home:
- Play "Qual or Quant?" in the car or at dinner: name something ("the colour of that truck", "how many stairs to our door") and have your child decide and explain.
- Turn questions around: ask your child to change a word question into a number question on the same topic.
Common difficulties:
- Thinking anything with a number is quantitative. Jersey numbers, room numbers and phone numbers are labels. Ask: "Would it make sense to add these?"
- Thinking a survey becomes quantitative because the votes were counted. The answers (skating, skiing) are qualitative; the counts are frequencies.
- Mixing kinds in one question ("tall" and "142 cm"). Encourage measuring everything the same way.