DoAssignment study guide

D1.2 · Collect and organize qualitative and quantitative data

Learn to collect and organize qualitative and quantitative data through clear examples and targeted practice.

Ontario Grade 6 Mathematics

Data

Grade 6 Mathematics — D1.2

Data is information we collect to answer a question. For example, a class might ask, “Which kind of book do you enjoy reading most?” The answers are information about the class. Before collecting data, decide what question you want to answer and what information will answer it. Then record the information carefully and organize it so another person can understand it.

What you will learn

Tell the difference between qualitative and quantitative data.
Collect information by asking a clear question and recording responses.
Organize data in a table so it is easier to read and check.

1. Choose a question and identify the data

Start with a question that is clear and can be answered by collecting information. “Which school subject do you enjoy most?” is clear if everyone is asked to name one subject. “What do you think about school?” is less clear because people could answer in many different ways.

Data means the information collected to answer a question. There are two useful kinds of data. Qualitative data tells about a quality or kind, such as a favourite subject or a book type. Quantitative data uses numbers to tell an amount or count, such as the number of books someone borrowed.

A number is not always quantitative data in the way we need for a question. For example, a locker number identifies a locker. It does not tell how many lockers someone has. Ask what the numbers mean before deciding how to organize them.

A response is one person’s answer or one recorded result. Decide what counts as one response before collecting information. If the question asks for one favourite subject, each person should give one subject. This makes the answers easier to sort and count.

Qualitative data describes a kind or quality.
Quantitative data gives a number that represents an amount or count.
A clear question helps people give responses that can be organized.

2. Collect and record responses carefully

Collecting data means gathering information. You might ask people a question, or you might record information that has already been provided. Keep the question and the responses together so it is clear what the information describes.

Record each response once and accurately. If someone gives an answer that is unclear, ask what they mean before recording it. Do not change a response to make it fit your guess. If a person does not answer, do not invent an answer for them.

A simple first record can be a list. For example, the following list is hypothetical. It shows answers from six learners to the question, “Which type of story would you choose?” The responses are adventure, mystery, adventure, comedy, mystery, and adventure.

A list preserves the responses, but repeated answers can be hard to scan. To organize the data, group matching answers and count how many times each answer appears. A table can show each category and its count. A category is a group name used to sort responses, such as “adventure.”

A list can preserve responses before they are grouped.
A category is a label for a group of matching responses.
Counts in an organized table should match the recorded responses.

3. Organize information so it is easy to use

A table uses rows and columns to arrange information. Give each column a heading that explains what belongs in it. For a question about story type, one column can show the type and another can show the number of responses.

When organizing qualitative data, put matching kinds of answers together. When organizing quantitative data, keep the numbers connected to what they count or measure. A heading such as “Number of books borrowed” is clearer than a heading that says only “Number.”

Check your organization against the original records. For a count table, add the category counts and compare the total with the number of responses recorded. If the totals do not agree, look for a response that was missed, counted twice, or placed in the wrong category.

An organized table does not change the information. It presents the same information in a form that is easier to read, compare, and check. Keep the question, category names, and units or descriptions clear enough that someone else can understand the table without guessing.

Use clear headings and category names.
Keep each number connected to what it represents.
Check that the organized information agrees with the original records.

Story-type responses

Story type	Number of responses
Adventure	3
Mystery	2
Comedy	1
Total	6

Weekly books borrowed

Number of books	Number of people
0	1
1	1
2	2
3	1
Total	5

Worked example

Group qualitative responses

Hypothetical data: Six learners answer, “Which type of story would you choose?” Their answers are adventure, mystery, adventure, comedy, mystery, and adventure. Organize the answers and check the total.

Identify the kind of data
The answers name kinds of stories. They describe a type, so this is qualitative data.
Group matching answers
Place the same answers in the same category. Adventure appears three times, mystery appears twice, and comedy appears once.
Check the count
The category counts represent all six responses. Add them to check that none was missed or counted twice.
$3+2+1=6$

Answer: The organized counts are adventure: 3, mystery: 2, and comedy: 1.

Check: The counts add to six, which matches the six responses in the original list.

Worked example

Organize quantitative data

Hypothetical data: A learner records the number of library books borrowed by five people in one week: 2, 0, 3, 2, and 1. Organize the information by number of books and check the total number of people.

Identify what the numbers mean
Each number tells how many books one person borrowed. The numbers represent counts, so this is quantitative data.
Group equal counts
There is one person with zero books, one with one book, two with two books, and one with three books. Include zero because it is a recorded response.
Check the number of records
Add the counts of people in the groups. The result should match the five people in the original list.
$1+1+2+1=5$

Answer: The organized data are: 0 books: 1 person; 1 book: 1 person; 2 books: 2 people; 3 books: 1 person.

Check: The group counts total five people. The table describes the same five recorded responses.

Worked example

Notice when data needs sorting

Hypothetical data: A group records preferred playground activities: skipping, drawing, tag, skipping, and tag. A learner says that the count for tag is three. Organize the list and decide whether the claim is correct.

Keep the response types clear
The activity names describe kinds of activities, so the data are qualitative. The category names should match the recorded answers.
Count each category in the list
Skipping appears twice, drawing appears once, and tag appears twice. Check each response rather than relying on a quick impression.
Compare with the claim
The claim says tag appears three times, but the list contains only two tag responses. The claim is not correct. The organized counts still add to five, the number of recorded answers.
$2+1+2=5$

Answer: The counts are skipping: 2, drawing: 1, and tag: 2. The claim that tag has three responses is incorrect.

Check: The three category counts account for all five responses, and the original list shows tag twice.

Common mistakes and how to avoid them

Changing a response to fit a category you expected.

Correction: Record what the person actually says. Ask for clarification if the response is unclear.

Leaving out a zero count or response.

Correction: Include every recorded answer, including zero when it is the answer.

Using headings that do not explain the numbers.

Correction: Name what is being counted or recorded so readers know what each number means.

Assuming the organized counts are correct without checking.

Correction: Compare the categories with the original responses and check that the total count matches.

Lesson summary

Data is information gathered to answer a question.
Qualitative data describes kinds or qualities; quantitative data uses numbers to show amounts or counts.
Record responses accurately, group matching information, and use clear table headings.
Check organized counts against the original records.

Check your understanding

Question 1

A class records each learner’s favourite fruit as apple, pear, or orange. What kind of data is this?

Qualitative, because the responses name kinds of fruit
Quantitative, because fruit choices can be counted
Quantitative, because each answer must be a number
It is not data because the answers are words

Show answer and explanation

Qualitative, because the responses name kinds of fruit

The responses name kinds of fruit. They describe categories, so they are qualitative data.

Question 2

A hypothetical list has the responses 1, 2, 1, 0, and 2. How many responses are in the group with the value 2?

Show answer and explanation

The value 2 appears twice in the list.

Question 3

A table groups five recorded answers. Its category counts are 2, 2, and 2. What should you do?

Accept the table because it has three categories
Change one count without checking
Check the original records because the counts total six, not five
Remove the smallest category

Show answer and explanation

Check the original records because the counts total six, not five

The category counts total six, but there are only five recorded answers. Recheck the records for a counting or organizing error.

Key terms

Data: Information collected to answer a question.
Qualitative data: Data that describes a kind or quality, such as a favourite activity.
Quantitative data: Data that uses numbers to show an amount or count.
Response: One person’s answer or one recorded result.
Category: A group name used to sort matching responses.

Continue through Grade 6 Math

View the complete Grade 6 Math Ontario Grade 6 Mathematics curriculum and lessons

About this lesson and its review

Published by DoAssignment. This reviewed lesson follows Ontario Grade 6 Mathematics, expectation D1.2. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

Official curriculum reference

Report a correction or ask a question