Grade by Grade
D. Data · Data Literacy and Probability

Collecting Data and Organizing It with Percentages

D1.2 D1.1 A1About 50 minutes
Learning goals
  • I can plan how to collect qualitative, discrete and continuous data to answer a question of interest.
  • I can decide whether to use a census or a sample, and how to choose a fair sample.
  • I can write survey questions that are fair and clear.
  • I can organize data in a frequency table with a percentage column, including data grouped in intervals.

Words to know

qualitative data
Data in words or categories, like favourite winter activity.
discrete data
Number data you count, like the number of pets. Only certain values are possible.
continuous data
Number data you measure, like time or height. Any value in a range is possible.
random sample
A sample where every member of the population has the same chance of being chosen, like drawing names from a hat.
biased
Unfair. A biased sample or question pushes the results one way.
interval
A range of values used to group number data, like 30 to less than 60 minutes.

Remember from Grade 6

You sorted data into qualitative, discrete and continuous, and you grouped number data into equal intervals in frequency tables. In the last lesson you learned why percentages help. Now you'll plan a whole data project and add a percentage column to your tables.

A question worth asking

The student council at Pine Hill Public School wants to plan a winter fun day. They ask, "What winter activity do Grade 7 students like best?" That is a question of interest: a real question that data can help answer.

Good data projects follow a plan:

  1. Ask a clear question of interest.
  2. Decide the population (who you want to learn about).
  3. Choose a census or a sample.
  4. Choose how to collect the data: a survey, measuring, or observing and counting.
  5. Organize the data in a table, with counts and percentages.
  6. Then graph it, analyse it and decide what to do (later lessons).
A snowy school yard with students skating on an outdoor rink, sledding down a hill and playing near a snow fort.
Skating, tobogganing and snow forts are all popular winter activities. A survey can tell the student council which one Grade 7 students like best. AI-generated image
1Aska question of interest2Populationwho do you want tolearn about?3Census or sample?everyone, or a fair part4Collectsurvey, measure orobserve5Organizetable with counts and%6Graph and decidelater lessons
The six steps of a data project, in order. Plan steps 1 to 4 before you collect anything, then organize your data with a percentage column.

Census or sample?

  • Use a census when the population is small and easy to reach, like the 24 students in your class or the 15 players on your team.
  • Use a sample when the population is big, or when checking everyone would take too long, cost too much, or use something up. Imagine testing every carton of milk by opening it! None would be left to sell.

A sample must be fair. In a random sample, everyone has the same chance of being picked, for example by drawing names from a container. A biased sample leaves some groups out, like surveying only your friends, or only the ski club about favourite winter activities.

Fair questions

The wording of a question can push people toward an answer. That makes the question biased.

  • Biased: "Don't you agree that skating is the best winter activity?"
  • Fair: "Which winter activity do you like best: skating, tobogganing, skiing, snowshoeing or building snow forts?"

Give answer choices that cover everyone, and add "other" if needed.

Random sampleski clubeveryone has the same chancefairBiased sampleski clubonly students in the ski clubunfair= picked
Filled dots are the students who get asked. A random sample spreads out across the whole population; a biased sample bunches up in one group, like the ski club, so its answers can't speak for everyone.
Worked example

Example 1: Organize qualitative data with percentages

The council surveys a random sample of 40 Grade 7 students. Skating 14, tobogganing 10, skiing 6, snowshoeing 4, building snow forts 6. Make a frequency table with a percentage column.

  1. Check the total: 14 + 10 + 6 + 4 + 6 = 40. ✓
  2. Each percentage is count ÷ 40 × 100. Since 40 × 2.5 = 100, you can also multiply each count by 2.5.
  3. Skating 14 × 2.5 = 35%. Tobogganing 10 × 2.5 = 25%. Skiing 6 × 2.5 = 15%. Snowshoeing 4 × 2.5 = 10%. Snow forts 6 × 2.5 = 15%.
  4. Check: 35 + 25 + 15 + 10 + 15 = 100%. ✓

See the table below. Skating is the favourite of the sample (35%), so the council might plan a skating event first.

Winter activityTally countPercentage
Skating1435%
Tobogganing1025%
Skiing615%
Snowshoeing410%
Building snow forts615%
Total40100%
Favourite winter activity of 40 Grade 7 students (random sample), Pine Hill P.S.
Worked example

Example 2: Continuous data in intervals

The council also asks, "How many minutes did you spend outside last Saturday?" Time is measured, so the data is continuous. The 25 answers are grouped in 30-minute intervals: 0 to less than 30: 3. 30 to less than 60: 7. 60 to less than 90: 8. 90 to less than 120: 5. 120 to less than 150: 2. Add a percentage column.

  1. Total: 3 + 7 + 8 + 5 + 2 = 25. ✓
  2. 25 × 4 = 100, so multiply each count by 4.
  3. 3 × 4 = 12%, 7 × 4 = 28%, 8 × 4 = 32%, 5 × 4 = 20%, 2 × 4 = 8%.
  4. Check: 12 + 28 + 32 + 20 + 8 = 100%. ✓

The interval 60 to less than 90 minutes has the greatest percentage (32%). Also, 20% + 8% = 28% of students were outside for 90 minutes or more.

Worked example

Example 3: Rounding percentages

Thirty families were asked how many pets they have. 0 pets: 11. 1 pet: 9. 2 pets: 7. 3 or more: 3. Find the percentages to the nearest whole percent.

  1. 0 pets: 11 ÷ 30 = 0.3666... ≈ 37%.
  2. 1 pet: 9 ÷ 30 = 0.30 = 30%.
  3. 2 pets: 7 ÷ 30 = 0.2333... ≈ 23%.
  4. 3 or more: 3 ÷ 30 = 0.10 = 10%.
  5. Check: 37 + 30 + 23 + 10 = 100%. ✓ (Sometimes rounded percentages add to 99% or 101%. That is okay. Write "Percentages are rounded." under the table.)

0 pets 37%, 1 pet 30%, 2 pets 23%, 3 or more 10%. This is discrete data, because pets are counted.

Plan before you collect

Write your plan in one sentence: "I will ask [question] to [census or random sample of how many] from [population], and record answers in a tally table." If you are working with a group, share the jobs and listen to each person's ideas. Good teamwork is part of doing math well.

Just for fun

Survey only the ski club about their favourite winter activity and you'll get a shocking result: skiing wins! That's a biased sample in action.

Hands-on activity

Window car-colour survey

You need: a window that looks onto a street or parking lot, or a walk with a grown-up (stay on the sidewalk), paper, a pencil and a calculator.

  1. Question of interest: "What colours are the cars that pass here?" This is qualitative data.
  2. Make a tally table with the categories white, black, grey or silver, red, blue and other.
  3. Tally the next 40 cars. (This is a sample of all the cars that use the street.)
  4. Add a percentage column. With 40 cars, each car is 2.5%.
  5. Check that your percentages add to about 100%.
  6. Now collect continuous data: with a timer, record how many seconds pass between cars, 10 times. Group your times in equal intervals.

Math talk: "Would you get the same results at a different time of day? Why might your sample be biased?"

Your turn

1

What type of data is it: "How many books did you read in March?"

2

What type of data is it: "How tall is your sunflower?"

3

What type of data is it: "Which language do you speak most at home?"

4

You want to know the T-shirt sizes of the 15 players on your team. Census or sample? Why?

5

Rewrite this biased question: "Don't you think recess should be longer?"

6

Twenty people answered: yes 13, no 5, not sure 2. Find the percentages.

7

Mia surveyed only the school's chess club to find students' favourite sport. Why is this a poor sample?

More practice: warm-up

1

Is "favourite season" qualitative or quantitative?

2

Is "the mass of a pumpkin" discrete or continuous?

3

Is "the number of goals in a game" discrete or continuous?

4

10 people were asked. 4 said yes. What percentage said yes?

5

You draw 30 names out of a hat that holds every student's name. What kind of sample is this?

More practice: on your own

1

Census or sample? (a) The heights of all the trees in a large provincial park. (b) The favourite lunches of 1 200 students. (c) Lunch orders for the 6 people in your family.

2

50 students were timed in a 1 km run. Under 5 min: 4. 5 to under 6 min: 11. 6 to under 7 min: 18. 7 to under 8 min: 12. 8 min or more: 5. Add a percentage column.

3

Is this a fair question? "How many hours of video games did you play last week: 0 to 2, 3 to 5, or 6 to 8?"

4

In a sample of 60 students, 21 have a library card. What percentage is that? About how many of the school's 480 students would you expect to have one?

5

Seven students were asked their favourite fruit: apple 3, banana 2, orange 2. Find the percentages, rounded to the nearest whole percent, and add them.

Challenge

1

In a survey, 25% of the people in a sample chose snowshoeing. That was 18 people. How many people were in the sample?

2

Plan a data project for the question "How long do Grade 7 students spend on homework each night?" Name the population, census or sample (and how you would choose it), the type of data, and how you would organize it.

3

A frequency table has 4 rows. The first three percentages are 18%, 34% and 29%. The total number of people is 300. How many people are in the fourth row?

Check your understanding

Quiz

1.

Which question collects continuous data?

2.

When is a census the best choice?

3.

Which sample is random?

4.

Which question is biased?

5.

In a sample of 25 people, 7 chose hot chocolate. What percentage is that?

6.

Rounded percentages in a table add to 101%. What is the most likely reason?

For parents and teachers

Big idea: The Ontario curriculum (D1.2) asks Grade 7 students to collect qualitative, discrete and continuous data to answer questions of interest and to organize the data, including using percentages. This lesson also looks at census versus sample and fair (random) samples, which help students explain where a percentage comes from (D1.1).

Common difficulties:

  • Mixing up discrete and continuous. Ask: "Did you count it or measure it?"
  • Writing leading questions or answer choices that leave people out.
  • Choosing a convenient sample (friends, one club) and calling it fair.
  • Worrying when rounded percentages add to 99% or 101%. That is normal; note "percentages are rounded".

How to help: Let your child run a small survey of family, neighbours or friends (with your permission) about a real question, then build the table together. Ask, "Who did you leave out? Would the answers change?" This lesson builds A1 skills: planning, working with others, and thinking critically about fairness.