Grade by Grade
D. Data · Data and Probability

Collecting Data: Questions, Tallies and Frequency Tables

D1.2 A1About 40 minutes
Learning goals
  • I can tell the difference between qualitative data (words) and quantitative data (numbers).
  • I can collect data by interviewing, observing or doing an experiment.
  • I can organize data in a frequency table.
  • I can write a good question to collect data.

Words to know

qualitative data
Data that is words or categories, like favourite sport or kind of tree.
quantitative data
Data that is numbers you count or measure, like how many pets or how tall.
interview
Collecting data by asking people a question.
observation
Collecting data by watching and counting, like counting birds at a feeder.
experiment
Collecting data by doing something on purpose and recording what happens, like rolling a number cube 20 times.
frequency
How many times something happens or is chosen.
frequency table
A table that shows each category or number and its frequency. It often has a tally column too.

Remember from Grade 2

In Grade 2 you collected data by interviewing, observing and experimenting, and you used tally marks in bundles of 5: four lines down and the fifth line across. In Grade 3 you'll look at two kinds of data and organize your data in frequency tables.

Data detectives need a question

Mr. Lavoie's Grade 3 class wants to plan a winter fun day. First they need to know: what do people like to do in the snow?

Every data project starts with a question of interest: a question you really want to answer. Then you collect data to answer it.

Two kinds of data

  • Qualitative data is words or categories. What is your favourite winter activity? Answers: skating, skiing...
  • Quantitative data is numbers you count or measure. How many times did you go skating this winter? Answers: 0, 3, 10...

A trick: quantitative sounds like quantity, which means how many or how much.

QuestionKind of dataWhy
What is your favourite season?QualitativeThe answers are words.
How many letters are in your first name?QuantitativeThe answers are numbers you count.
How tall is your snow fort, in centimetres?QuantitativeThe answers are numbers you measure.
What kind of tree is in your yard?QualitativeThe answers are words, like maple or spruce.
Qualitative or quantitative?

Three ways to collect data

  1. Interview: ask people a question. "What is your favourite winter activity?"
  2. Observation: watch and count. Count the kinds of birds that visit a feeder in 15 minutes.
  3. Experiment: do something on purpose and record what happens. Roll a number cube 20 times and record each number.

Frequency tables

As you collect, make one tally mark for each answer. Then count the tallies and write the number. That number is the frequency. A table with the categories, tallies and frequencies is a frequency table.

Our Favourite Winter ActivityActivityTallyFrequencySkating8Tobogganing7Snow forts5Skiing4
Frequency table: Our Favourite Winter Activity. Source: interviews with Mr. Lavoie's Grade 3 class. Skating 8, tobogganing 7, snow forts 5, skiing 4.
Worked example

Example 1: An interview (qualitative data)

The class asked everyone, "What is your favourite winter activity? Choose one." Use the frequency table. How many people answered? Which activity was chosen most?

  1. Read each frequency: skating 8, tobogganing 7, snow forts 5, skiing 4.
  2. Add them: 8 + 7 = 15, 15 + 5 = 20, 20 + 4 = 24.
  3. The biggest frequency is 8, for skating.

24 people answered. Skating was chosen most often. The data is qualitative because the answers are words.

Worked example

Example 2: An experiment (quantitative data)

Zoe rolled a number cube 20 times and recorded each number in a frequency table. How many times did she roll a number greater than 4?

  1. Greater than 4 means 5 or 6.
  2. Frequency of 5: 3. Frequency of 6: 3.
  3. 3 + 3 = 6.
  4. Check the whole table: 3 + 4 + 2 + 5 + 3 + 3 = 20 rolls. That matches.

She rolled a number greater than 4 6 times. This data is quantitative: the results are numbers.

Rolling a Number Cube 20 TimesNumber rolledTallyFrequency132432455363
Frequency table from Zoe's experiment. Source: Zoe's 20 rolls of a number cube.
Worked example

Example 3: An observation

Raj sat by the window for 10 minutes on a fall afternoon and recorded each vehicle that went by: car, car, truck, bus, car, bike, car, truck, car, bike. Make a frequency table.

  1. Make a tally mark for each vehicle as you read the list.
  2. Car: 1, 2, 3, 4, 5. That's 5.
  3. Truck: 2. Bus: 1. Bike: 2.
  4. Check: 5 + 2 + 1 + 2 = 10, and the list has 10 vehicles.

Car 5, Truck 2, Bus 1, Bike 2. Total: 10 vehicles. This is qualitative data: the categories are words.

VehicleTallyFrequency
Car5 (one full bundle)5
Truck2 lines2
Bus1 line1
Bike2 lines2
Raj's frequency table. Source: Raj's observation, 10 minutes at the window.

How to write a good survey question

  • Make it clear so everyone understands it the same way.
  • Say "Choose one" if you want one answer from each person.
  • Give choices if you can, and add other for answers you didn't think of.
  • Ask each person only once, and keep a list so you don't miss anyone.

Being a respectful data collector

When you interview people, be polite, wait your turn and listen. It is okay if someone does not want to answer. Every answer counts the same, even if it is different from yours.

Just for fun

What has four sticks standing up and one lying across them, but is not a fence?

A tally for 5!

Hands-on activity

Your own data project

Pick one of these:

  • Interview: ask 10 family members, friends or neighbours, "What is your favourite season? Choose one." (qualitative)
  • Experiment: flip a coin 20 times and record heads or tails. Or roll a number cube 20 times. (A grown-up should help if younger children are near: coins and dice are small and can be a choking risk.)
  • Observation: look out the window for 10 minutes and record each kind of vehicle or bird you see.

Then:

  1. Make a frequency table with three columns: category or number, tally, frequency.
  2. Add a title and a source (who collected it, and how).
  3. Check that your frequencies add up to the number of answers.

Math talk: "Is my data qualitative or quantitative? How do I know?"

Your turn

1

Is favourite fruit qualitative or quantitative data?

2

Is the number of teeth you have lost qualitative or quantitative data?

3

Lena watches a bird feeder and records each kind of bird that lands. Is this an interview, an observation or an experiment?

4

What number do these tallies show: two bundles of 5 and 3 more lines?

5

Use the winter activity table. How many people chose snow forts or skiing?

6

Ty asked, "What's your favourite sport?" Some people named two sports, and he didn't know how to tally them. How could he make his question better?

More practice: warm-up

1

What does frequency mean?

2

How do you show 7 with tally marks?

3

Is your height in centimetres qualitative or quantitative?

4

Is your favourite season qualitative or quantitative?

5

You ask your friends a question and record their answers. Which way of collecting data is this?

More practice: on your own

1

Make a frequency table for these favourite pets: dog, cat, dog, fish, dog, cat, bird, dog, cat, dog, fish, cat.

2

Ten children said how many pets they have: 0, 1, 2, 1, 0, 3, 1, 1, 2, 0. Make a frequency table. Is this data qualitative or quantitative?

3

You want to know: Which kind of ball bounces highest? Would you use an interview, an observation or an experiment? Explain.

4

A Grade 3 class has 26 students. Their frequency table adds up to 25. What might have happened?

5

Write a question about winter that gives quantitative data.

Challenge

1

Owen's frequency table shows: apple 6, banana ?, orange 4. He surveyed 17 people. How many chose banana?

2

In Zoe's 20 rolls, a 4 came up 5 times but a 3 came up only 2 times. Zoe says, "This number cube must be unfair." Do you agree? What could she do to find out?

3

Write one question about your class that gives qualitative data and one that gives quantitative data. Say how you would collect each.

Check your understanding

Quiz

1.

Which question gives quantitative data?

2.

Counting the birds that land at a feeder is...

3.

Two bundles of 5 tallies and 1 more line show which number?

4.

In a frequency table, the frequency is...

5.

Skating 8, tobogganing 7, snow forts 5, skiing 4. How many people were surveyed?

6.

Rolling a toy car down a ramp 10 times and measuring how far it goes each time is...

For parents and teachers

What your child is learning: to collect data through interviews, observations and experiments to answer questions they care about, to tell qualitative data (words or categories) from quantitative data (numbers counted or measured), and to organize data in frequency tables (Ontario expectation D1.2). Planning, being respectful when interviewing and checking work connect to the social-emotional learning skills in Strand A.

Common difficulties:

  • Mixing up the two words. "Quantitative" sounds like quantity (how many).
  • Thinking any answer with a number in it is quantitative. "What is your favourite number?" has number answers, but they are really labels; this is a good thing to talk about together.
  • Losing count while tallying. Cross off each answer on the list once it is tallied, and always check that the frequencies add up to the total.
  • Questions that allow more than one answer. Add "Choose one".

At home: let your child run a short survey of family or friends (by phone or video is fine), or record an experiment like 20 coin flips. Supervise small objects like coins and dice around younger children.