D. Data · Data and Probability

Collecting Data and Relative-Frequency Tables

D1.2 D1.1 A1About 45 minutes

Learning goals

I can plan how to collect data to answer a question about a population.
I can find the relative frequency of each category as a fraction and as a decimal.
I can organize data in a relative-frequency table and check that the relative frequencies add to 1.
I can use relative frequencies to compare groups of different sizes and to make predictions.

Words to know

frequency
How many times something happens or is chosen.

relative frequency
The frequency divided by the total. It tells what fraction of the whole data set is in one category.

relative-frequency table
A table that shows the frequency and the relative frequency of each category.

observation
Collecting data by watching and recording, like counting birds at a feeder.

experiment
Collecting data by testing something and recording the results.

interview
Collecting data by asking people questions and recording their answers.

Remember from Grade 4

You organized data in frequency tables and collected data from primary sources (surveys, observations, experiments) and secondary sources (data someone else collected, like a government website). Now you'll add a new column that makes comparing much fairer.

Which class has more walkers?

In Room 5, 12 students walk to school. In Room 6, 15 students walk. So Room 6 has more walkers, right?

Wait. Room 5 has 24 students and Room 6 has 30.

Room 5: 12 out of 24 walk. That's 12/24 = 1/2 of the class.
Room 6: 15 out of 30 walk. That's 15/30 = 1/2 of the class.

Both classes have the same share of walkers! Comparing parts of the whole is fairer when groups are different sizes. That's what relative frequency does.

Each bar is one whole class. Room 6 has more walkers, but in both rooms the shaded walkers fill exactly half of the bar: 12/24 = 15/30 = 1/2.

Relative frequency

Relative frequency = frequency ÷ total

Write it as a fraction: frequency over total. Then you can also write it as a decimal. To get a decimal, make an equivalent fraction out of 10 or out of 100.

5 out of 20 → 5/20 = 25/100 = 0.25
8 out of 20 → 8/20 = 40/100 = 0.40

The relative frequencies of all the categories add to 1, because all the parts together make 1 whole data set.

Plan, collect, organize

Ask a question about a population. What is the favourite winter activity of the junior students (Grades 4 to 6) at our school?
Choose a sample if the population is big. There are 200 junior students. The class takes a systematic random sample of 20: every 10th name on the list after a random start.
Collect the data. You might use an interview or survey, an observation, an experiment, or a secondary source.
Organize the data in a relative-frequency table.

Activity	Frequency	Relative frequency (fraction)	Relative frequency (decimal)
Skating	5	5/20 = 1/4	0.25
Sledding	8	8/20 = 2/5	0.40
Skiing	3	3/20	0.15
Snowshoeing	4	4/20 = 1/5	0.20
Total	20	20/20 = 1	1.00

Favourite winter activity of a sample of 20 junior students. Source: class interviews, January 2026.

The relative frequencies are shares of one whole strip. The numbers under the strip add up as you go, and the last one is 1, because the parts make the whole sample.

Using the table to predict

The sample was chosen fairly, so it should be representative. In the sample, 8 out of every 20 students chose sledding.

The population has 200 students. 200 is 10 groups of 20, so about 10 × 8 = 80 junior students would choose sledding. This is a prediction, not an exact count.

Worked example

Example 1: Make a relative-frequency table

Mila observed the birds at her feeder for one morning: chickadees 6, blue jays 2, cardinals 1, sparrows 1. Make a relative-frequency table.

Find the total: 6 + 2 + 1 + 1 = 10 birds.
Chickadees: 6/10 = 0.6
Blue jays: 2/10 = 0.2
Cardinals: 1/10 = 0.1. Sparrows: 1/10 = 0.1.
Check: 0.6 + 0.2 + 0.1 + 0.1 = 1.0 ✓

Chickadees 0.6, blue jays 0.2, cardinals 0.1, sparrows 0.1. Mila collected this data by observation.

Worked example

Example 2: Compare groups of different sizes

In Room 3 (25 students), 10 chose hot chocolate as their favourite winter drink. In Room 7 (20 students), 9 chose hot chocolate. Which class has the greater share choosing hot chocolate?

Room 3: 10/25. Multiply top and bottom by 4: 40/100 = 0.40.
Room 7: 9/20. Multiply top and bottom by 5: 45/100 = 0.45.
0.45 is greater than 0.40.

Room 7 has the greater share (0.45), even though fewer students (9) chose hot chocolate.

Working together

Before you collect data, check your question with a partner. Is it clear? Could anyone feel uncomfortable answering? Good data collectors are respectful: they ask kindly, let people say "I'd rather not answer," and keep answers private when they should.

Just for fun

Why did the chickadees have the biggest relative frequency at Mila's feeder?

They told all their friends about the free snacks!

Hands-on activity

Collect and organize your own data

Choose one of these:

Observation: From a window at home, record the colour of the next 20 cars that go by. (Stay inside or stay with a grown-up near any road.)
Interview: Ask 20 family members, neighbours or friends (with your grown-up's help, in person or by phone) one question, like "What is your favourite season?"
Experiment: Drop a paper cup 20 times from the same height and record whether it lands on its side, its top or its bottom.

Then:

Make a relative-frequency table with a fraction column and a decimal column. (Using 20 makes the decimals friendly: multiply top and bottom by 5.)
Check that the relative frequencies add to 1.
Write one sentence that uses a relative frequency, like "0.35 of the cars were white."

Your turn

A sample of 10 students named their pets: dog 4, cat 3, fish 1, no pet 2. What is the relative frequency of dog, as a fraction and a decimal?

Using the same data, what is the relative frequency of cat?

What do all the relative frequencies in that table add up to?

In a sample of 50 students, 20 walk to school. What is the relative frequency of walking?

Counting birds at a feeder is which way of collecting data: interview, observation, experiment or secondary source?

Class A: 12 of 24 students like winter best. Class B: 15 of 25 like winter best. Which class has the greater share?

In a fair sample of 20 students, 5 chose skating. The school has 300 students. About how many would choose skating?

More practice: warm-up

7 out of 10 chose apples. Write the relative frequency as a fraction and a decimal.

Write 1/4 as a decimal.

Write 3/5 as a decimal.

The relative frequencies in a complete table add up to ______.

Looking up last winter's snowfall on a government weather website is which kind of source?

More practice: on your own

25 students named their usual breakfast: cereal 10, toast 8, eggs 4, other 3. Find each relative frequency as a decimal.

40 people chose a fruit. The relative frequency of apple is 0.5 and of orange is 0.25. Everyone else chose banana. How many chose banana?

Why is relative frequency better than frequency for comparing a class of 20 and a class of 30?

Rafi drops a paper cup 20 times. It lands on its side 14 times. What is the relative frequency of landing on its side?

Write a question about the population "students in my school" and say how you would choose a fair sample.

Challenge

In a Grade 4 sample, 15 of 20 students want a winter carnival. In a Grade 6 sample, 18 of 25 do. Which sample shows the greater share wanting a carnival?

In a relative-frequency table, skating has frequency 6 and relative frequency 0.3. Sledding has relative frequency 0.45. The only other category is skiing. Find the total, the frequency of sledding, and the frequency and relative frequency of skiing.

A fair sample of 25 students is taken from a school of 500. In the sample, 4 chose snowshoeing. Predict how many students in the school would choose snowshoeing. Will the real number be exactly that?

Check your understanding

Quiz

6 of 20 students chose skiing. What is the relative frequency of skiing?

In a complete relative-frequency table, the relative frequencies add up to:

Which is a secondary source?

Class A: 10 of 20 chose sledding. Class B: 12 of 30 chose sledding. Which class has the greater share?

What is 2/5 as a decimal?

In a fair sample of 10 students, 3 chose hockey. About how many of 200 students would choose hockey?

For parents and teachers

What this lesson teaches: planning a data collection about a population (using a sample when needed), collecting data by interview, observation, experiment or secondary source, and organizing it in a relative-frequency table (D1.2), with links to sampling (D1.1). Respectful data collection (A1) is built in.

How to help at home:

Use samples of 10, 20, 25 or 50. These make the decimals easy (multiply to get a denominator of 100).
When comparing two groups, ask, "Are the groups the same size? What share of each group?"
Do the data-collection activity together and post the table on the fridge.

Common difficulties:

Writing the frequency instead of the relative frequency (writing 8 instead of 8/20).
Dividing the wrong way (20/8 instead of 8/20). Say it as "part out of the whole".
Forgetting to check that the relative frequencies add to 1.
Treating a prediction from a sample as an exact count. Use words like "about".