D1.2 · Collect and organize qualitative and quantitative data using percentages

Ontario Grade 7 Mathematics

Data

Grade 7 Mathematics · D1.2

What you will learn

• Collect qualitative or quantitative data by asking a clear question and recording responses.
• Organize responses into categories and find how many belong in each category.
• Use percentages to show how each category compares with the total.

1. Choose a question and collect data

• Qualitative data name or describe groups.
• Quantitative data are counts or measurements.
• A tally records each response once.

2. Organize responses into categories

• A category sorts responses into a group.
• Frequency means the number of responses in a category.
• The category frequencies should add to the total number of responses.

3. Find and use percentages

• Percentage = category frequency divided by total frequency, then multiplied by 100.
• Use the whole data set as the total.
• Label the categories and state that the display shows percentages.

Example 1: Organizing poll responses

Worked example

Example 1: Qualitative data from a class poll

1. Identify the data
   The answers are activity names, so they are qualitative data. Each activity is a category. The given counts are the frequencies.
2. Check the total
   Add the three frequencies. They add to 20, which matches the number of students in the poll.
   $$8 + 7 + 5 = 20$$
3. Find each percentage
   Compare each category's frequency with the total of 20. For art, 8 divided by 20 is 0.4, or 40 percent. Use the same total for the other categories.
   $$\frac{8}{20}\times100\%=40\%,\quad \frac{7}{20}\times100\%=35\%,\quad \frac{5}{20}\times100\%=25\%$$

Worked example

Example 2: Quantitative data organized in ranges

1. Identify the data and categories
   Reading time is measured in minutes, so it is quantitative data. The ranges are the categories. Each student belongs in the range that includes their reading time.
2. Confirm the total
   Add the frequencies to check that all 20 students are counted.
   $$5 + 10 + 5 = 20$$
3. Convert each frequency to a percentage
   Use 20 as the total each time. Five out of 20 is 25 percent, and ten out of 20 is 50 percent.
   $$\frac{5}{20}\times100\%=25\%,\quad \frac{10}{20}\times100\%=50\%,\quad \frac{5}{20}\times100\%=25\%$$

Worked example

Example 3: Organize a small set of numeric responses

1. Count each response
   The answers are numbers, so they are quantitative data. Count how often each number appears. There are four 0s, four 1s, three 2s, and one 3.
   $$4 + 4 + 3 + 1 = 12$$
2. Use 12 as the total
   The total is 12 because 12 students answered. Divide each frequency by 12 and multiply by 100. The results include repeating decimal values, so round to the nearest whole percent.
   $$\frac{4}{12}\times100\%\approx33\%,\quad \frac{3}{12}\times100\%=25\%,\quad \frac{1}{12}\times100\%\approx8\%$$
3. Report the organized results
   The rounded percentages show the share of students in each group. Because the values were rounded, their sum may differ slightly from 100 percent.
   $$33\% + 33\% + 25\% + 8\% = 99\%$$

Common mistakes and how to avoid them

Lesson summary

• Collect answers by asking a clear question and recording each response.
• Qualitative data use names or descriptions; quantitative data use numbers.
• Organize responses into categories and count each category's frequency.
• Find a category percentage by dividing its frequency by the total and multiplying by 100.
• Check the total and label any display clearly. Rounded percentages may not add to exactly 100%.

Check your understanding

Key terms

Data

Facts or answers collected to learn about a question.

Qualitative data

Data that name or describe a group or quality.

Quantitative data

Data written as numbers, such as counts or measurements.

Category

A group used to sort responses.

Frequency

The number of responses in a category.

Percentage

A way to describe an amount out of 100.

Tally

A quick mark used to record one response.

Continue through Grade 7 Math

View the complete Grade 7 Math Ontario Grade 7 Mathematics curriculum and lessons

• D1.1 · Explain percent distributions of large populations and samples
• D1.3 · Select suitable graphs, including circle graphs
• D1.4 · Create a data infographic with tables and circle graphs
• D1.6 · Critique circle graphs and misleading displays before drawing conclusions
• D2.2 · Compare theoretical and experimental probabilities for two events
• B1.1 · Represent and compare whole numbers up to one billion using powers of ten

About this lesson and its review

Published by DoAssignment. This reviewed lesson follows Ontario Grade 7 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

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