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Chapter 49: Data Collection, Sampling, and Bias

Learn Grade 8 Math from beginner foundations through advanced Grade 8 problem solving with detailed explanations, at least five examples per topic, practice exercises, and review questions.

Grade 8Beginner Friendly5+ Examples Per TopicPractice30 Q&A
Estimated reading time0% read
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What this chapter covers

This chapter contains 14 topics. Technical terms are followed by plain-language meanings where they first appear. Each topic includes at least five worked examples. Coding is included only where it naturally supports the Grade 8 coding expectations.

49.1 Data

Data are observations, measurements, or categories collected to answer questions. In this section, the focus is Data.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Classify this data set: [4, 6, 8].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 2

Problem: Classify this data set: [5, 9, 10, 12].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 3

Problem: Classify this data set: [3, 7, 7, 11].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 4

Problem: Classify this data set: [20, 25, 30].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 5

Problem: Classify this data set: [6, 8, 9, 12, 15].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 6

Problem: Classify this data set: [2, 4, 4, 5, 20].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 7

Problem: Classify this data set: [10, 11, 12, 13, 14].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 8

Problem: Classify this data set: [1, 3, 5, 7, 9].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 9

Problem: Classify this data set: [8, 8, 8, 9, 10].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 10

Problem: Classify this data set: [15, 18, 21, 24, 27].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Practice exercise

Create one new Grade 8 problem involving Data. Show the important steps, include units when needed, and explain how you checked the answer.

49.2 Qualitative data

Data are observations, measurements, or categories collected to answer questions. In this section, the focus is Qualitative data.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Classify this data set: [4, 6, 8].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 2

Problem: Classify this data set: [5, 9, 10, 12].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 3

Problem: Classify this data set: [3, 7, 7, 11].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 4

Problem: Classify this data set: [20, 25, 30].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 5

Problem: Classify this data set: [6, 8, 9, 12, 15].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 6

Problem: Classify this data set: [2, 4, 4, 5, 20].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 7

Problem: Classify this data set: [10, 11, 12, 13, 14].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 8

Problem: Classify this data set: [1, 3, 5, 7, 9].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 9

Problem: Classify this data set: [8, 8, 8, 9, 10].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 10

Problem: Classify this data set: [15, 18, 21, 24, 27].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Practice exercise

Create one new Grade 8 problem involving Qualitative data. Show the important steps, include units when needed, and explain how you checked the answer.

49.3 Quantitative data

Data are observations, measurements, or categories collected to answer questions. In this section, the focus is Quantitative data.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Classify this data set: [4, 6, 8].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 2

Problem: Classify this data set: [5, 9, 10, 12].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 3

Problem: Classify this data set: [3, 7, 7, 11].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 4

Problem: Classify this data set: [20, 25, 30].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 5

Problem: Classify this data set: [6, 8, 9, 12, 15].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 6

Problem: Classify this data set: [2, 4, 4, 5, 20].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 7

Problem: Classify this data set: [10, 11, 12, 13, 14].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 8

Problem: Classify this data set: [1, 3, 5, 7, 9].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 9

Problem: Classify this data set: [8, 8, 8, 9, 10].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 10

Problem: Classify this data set: [15, 18, 21, 24, 27].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Practice exercise

Create one new Grade 8 problem involving Quantitative data. Show the important steps, include units when needed, and explain how you checked the answer.

49.4 Discrete data

Data are observations, measurements, or categories collected to answer questions. In this section, the focus is Discrete data.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Classify this data set: [4, 6, 8].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 2

Problem: Classify this data set: [5, 9, 10, 12].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 3

Problem: Classify this data set: [3, 7, 7, 11].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 4

Problem: Classify this data set: [20, 25, 30].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 5

Problem: Classify this data set: [6, 8, 9, 12, 15].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 6

Problem: Classify this data set: [2, 4, 4, 5, 20].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 7

Problem: Classify this data set: [10, 11, 12, 13, 14].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 8

Problem: Classify this data set: [1, 3, 5, 7, 9].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 9

Problem: Classify this data set: [8, 8, 8, 9, 10].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 10

Problem: Classify this data set: [15, 18, 21, 24, 27].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Practice exercise

Create one new Grade 8 problem involving Discrete data. Show the important steps, include units when needed, and explain how you checked the answer.

49.5 Continuous data

Data are observations, measurements, or categories collected to answer questions. In this section, the focus is Continuous data.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Classify this data set: [4, 6, 8].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 2

Problem: Classify this data set: [5, 9, 10, 12].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 3

Problem: Classify this data set: [3, 7, 7, 11].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 4

Problem: Classify this data set: [20, 25, 30].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 5

Problem: Classify this data set: [6, 8, 9, 12, 15].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 6

Problem: Classify this data set: [2, 4, 4, 5, 20].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 7

Problem: Classify this data set: [10, 11, 12, 13, 14].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 8

Problem: Classify this data set: [1, 3, 5, 7, 9].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 9

Problem: Classify this data set: [8, 8, 8, 9, 10].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 10

Problem: Classify this data set: [15, 18, 21, 24, 27].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Practice exercise

Create one new Grade 8 problem involving Continuous data. Show the important steps, include units when needed, and explain how you checked the answer.

49.6 Primary data

Data are observations, measurements, or categories collected to answer questions. In this section, the focus is Primary data.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Classify this data set: [4, 6, 8].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 2

Problem: Classify this data set: [5, 9, 10, 12].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 3

Problem: Classify this data set: [3, 7, 7, 11].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 4

Problem: Classify this data set: [20, 25, 30].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 5

Problem: Classify this data set: [6, 8, 9, 12, 15].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 6

Problem: Classify this data set: [2, 4, 4, 5, 20].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 7

Problem: Classify this data set: [10, 11, 12, 13, 14].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 8

Problem: Classify this data set: [1, 3, 5, 7, 9].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 9

Problem: Classify this data set: [8, 8, 8, 9, 10].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 10

Problem: Classify this data set: [15, 18, 21, 24, 27].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Practice exercise

Create one new Grade 8 problem involving Primary data. Show the important steps, include units when needed, and explain how you checked the answer.

49.7 Secondary data

Data are observations, measurements, or categories collected to answer questions. In this section, the focus is Secondary data.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Classify this data set: [4, 6, 8].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 2

Problem: Classify this data set: [5, 9, 10, 12].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 3

Problem: Classify this data set: [3, 7, 7, 11].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 4

Problem: Classify this data set: [20, 25, 30].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 5

Problem: Classify this data set: [6, 8, 9, 12, 15].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 6

Problem: Classify this data set: [2, 4, 4, 5, 20].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 7

Problem: Classify this data set: [10, 11, 12, 13, 14].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 8

Problem: Classify this data set: [1, 3, 5, 7, 9].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 9

Problem: Classify this data set: [8, 8, 8, 9, 10].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 10

Problem: Classify this data set: [15, 18, 21, 24, 27].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Practice exercise

Create one new Grade 8 problem involving Secondary data. Show the important steps, include units when needed, and explain how you checked the answer.

49.8 Population

A population is the entire group being studied. In this section, the focus is Population.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Classify this data set: [4, 6, 8].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 2

Problem: Classify this data set: [5, 9, 10, 12].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 3

Problem: Classify this data set: [3, 7, 7, 11].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 4

Problem: Classify this data set: [20, 25, 30].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 5

Problem: Classify this data set: [6, 8, 9, 12, 15].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 6

Problem: Classify this data set: [2, 4, 4, 5, 20].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 7

Problem: Classify this data set: [10, 11, 12, 13, 14].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 8

Problem: Classify this data set: [1, 3, 5, 7, 9].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 9

Problem: Classify this data set: [8, 8, 8, 9, 10].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 10

Problem: Classify this data set: [15, 18, 21, 24, 27].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Practice exercise

Create one new Grade 8 problem involving Population. Show the important steps, include units when needed, and explain how you checked the answer.

49.9 Sample

A sample is a smaller group selected from a population. In this section, the focus is Sample.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Classify this data set: [4, 6, 8].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 2

Problem: Classify this data set: [5, 9, 10, 12].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 3

Problem: Classify this data set: [3, 7, 7, 11].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 4

Problem: Classify this data set: [20, 25, 30].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 5

Problem: Classify this data set: [6, 8, 9, 12, 15].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 6

Problem: Classify this data set: [2, 4, 4, 5, 20].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 7

Problem: Classify this data set: [10, 11, 12, 13, 14].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 8

Problem: Classify this data set: [1, 3, 5, 7, 9].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 9

Problem: Classify this data set: [8, 8, 8, 9, 10].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 10

Problem: Classify this data set: [15, 18, 21, 24, 27].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Practice exercise

Create one new Grade 8 problem involving Sample. Show the important steps, include units when needed, and explain how you checked the answer.

49.10 Representative sample

A sample is a smaller group selected from a population. In this section, the focus is Representative sample.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Classify this data set: [4, 6, 8].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 2

Problem: Classify this data set: [5, 9, 10, 12].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 3

Problem: Classify this data set: [3, 7, 7, 11].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 4

Problem: Classify this data set: [20, 25, 30].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 5

Problem: Classify this data set: [6, 8, 9, 12, 15].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 6

Problem: Classify this data set: [2, 4, 4, 5, 20].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 7

Problem: Classify this data set: [10, 11, 12, 13, 14].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 8

Problem: Classify this data set: [1, 3, 5, 7, 9].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 9

Problem: Classify this data set: [8, 8, 8, 9, 10].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 10

Problem: Classify this data set: [15, 18, 21, 24, 27].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Practice exercise

Create one new Grade 8 problem involving Representative sample. Show the important steps, include units when needed, and explain how you checked the answer.

49.11 Random sampling

Random sampling is an important Grade 8 concept in Data Collection, Sampling, and Bias. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Classify this data set: [4, 6, 8].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 2

Problem: Classify this data set: [5, 9, 10, 12].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 3

Problem: Classify this data set: [3, 7, 7, 11].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 4

Problem: Classify this data set: [20, 25, 30].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 5

Problem: Classify this data set: [6, 8, 9, 12, 15].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 6

Problem: Classify this data set: [2, 4, 4, 5, 20].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 7

Problem: Classify this data set: [10, 11, 12, 13, 14].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 8

Problem: Classify this data set: [1, 3, 5, 7, 9].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 9

Problem: Classify this data set: [8, 8, 8, 9, 10].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 10

Problem: Classify this data set: [15, 18, 21, 24, 27].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Practice exercise

Create one new Grade 8 problem involving Random sampling. Show the important steps, include units when needed, and explain how you checked the answer.

49.12 Sampling bias

Bias is an influence that can make data collection or conclusions unrepresentative. In this section, the focus is Sampling bias.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Classify this data set: [4, 6, 8].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 2

Problem: Classify this data set: [5, 9, 10, 12].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 3

Problem: Classify this data set: [3, 7, 7, 11].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 4

Problem: Classify this data set: [20, 25, 30].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 5

Problem: Classify this data set: [6, 8, 9, 12, 15].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 6

Problem: Classify this data set: [2, 4, 4, 5, 20].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 7

Problem: Classify this data set: [10, 11, 12, 13, 14].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 8

Problem: Classify this data set: [1, 3, 5, 7, 9].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 9

Problem: Classify this data set: [8, 8, 8, 9, 10].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 10

Problem: Classify this data set: [15, 18, 21, 24, 27].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Practice exercise

Create one new Grade 8 problem involving Sampling bias. Show the important steps, include units when needed, and explain how you checked the answer.

49.13 Survey-question bias

Bias is an influence that can make data collection or conclusions unrepresentative. In this section, the focus is Survey-question bias.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Classify this data set: [4, 6, 8].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 2

Problem: Classify this data set: [5, 9, 10, 12].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 3

Problem: Classify this data set: [3, 7, 7, 11].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 4

Problem: Classify this data set: [20, 25, 30].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 5

Problem: Classify this data set: [6, 8, 9, 12, 15].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 6

Problem: Classify this data set: [2, 4, 4, 5, 20].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 7

Problem: Classify this data set: [10, 11, 12, 13, 14].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 8

Problem: Classify this data set: [1, 3, 5, 7, 9].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 9

Problem: Classify this data set: [8, 8, 8, 9, 10].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 10

Problem: Classify this data set: [15, 18, 21, 24, 27].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Practice exercise

Create one new Grade 8 problem involving Survey-question bias. Show the important steps, include units when needed, and explain how you checked the answer.

49.14 Ethical data collection

Data are observations, measurements, or categories collected to answer questions. In this section, the focus is Ethical data collection.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Classify this data set: [4, 6, 8].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 2

Problem: Classify this data set: [5, 9, 10, 12].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 3

Problem: Classify this data set: [3, 7, 7, 11].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 4

Problem: Classify this data set: [20, 25, 30].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 5

Problem: Classify this data set: [6, 8, 9, 12, 15].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 6

Problem: Classify this data set: [2, 4, 4, 5, 20].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 7

Problem: Classify this data set: [10, 11, 12, 13, 14].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 8

Problem: Classify this data set: [1, 3, 5, 7, 9].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 9

Problem: Classify this data set: [8, 8, 8, 9, 10].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Worked Example 10

Problem: Classify this data set: [15, 18, 21, 24, 27].

  1. The values are numerical.
  2. Ask whether they are counts or measurements.

Very beginner explanation: Quantitative data are numbers that represent counts or measurements.

Answer: Quantitative data

Practice exercise

Create one new Grade 8 problem involving Ethical data collection. Show the important steps, include units when needed, and explain how you checked the answer.

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Chapter 49 Review Questions and Answers

Q1. What is important to remember about Data?

Answer: Data are observations, measurements, or categories collected to answer questions. In this section, the focus is Data.

Q2. What is important to remember about Qualitative data?

Answer: Data are observations, measurements, or categories collected to answer questions. In this section, the focus is Qualitative data.

Q3. What is important to remember about Quantitative data?

Answer: Data are observations, measurements, or categories collected to answer questions. In this section, the focus is Quantitative data.

Q4. What is important to remember about Discrete data?

Answer: Data are observations, measurements, or categories collected to answer questions. In this section, the focus is Discrete data.

Q5. What is important to remember about Continuous data?

Answer: Data are observations, measurements, or categories collected to answer questions. In this section, the focus is Continuous data.

Q6. What is important to remember about Primary data?

Answer: Data are observations, measurements, or categories collected to answer questions. In this section, the focus is Primary data.

Q7. What is important to remember about Secondary data?

Answer: Data are observations, measurements, or categories collected to answer questions. In this section, the focus is Secondary data.

Q8. What is important to remember about Population?

Answer: A population is the entire group being studied. In this section, the focus is Population.

Q9. What is important to remember about Sample?

Answer: A sample is a smaller group selected from a population. In this section, the focus is Sample.

Q10. What is important to remember about Representative sample?

Answer: A sample is a smaller group selected from a population. In this section, the focus is Representative sample.

Q11. What is important to remember about Random sampling?

Answer: Random sampling is an important Grade 8 concept in Data Collection, Sampling, and Bias. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q12. What is important to remember about Sampling bias?

Answer: Bias is an influence that can make data collection or conclusions unrepresentative. In this section, the focus is Sampling bias.

Q13. What is important to remember about Survey-question bias?

Answer: Bias is an influence that can make data collection or conclusions unrepresentative. In this section, the focus is Survey-question bias.

Q14. What is important to remember about Ethical data collection?

Answer: Data are observations, measurements, or categories collected to answer questions. In this section, the focus is Ethical data collection.

Q15. Why should you show your steps?

Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.

Q16. Why is estimation useful?

Answer: Estimation helps you judge whether a calculated answer is reasonable.

Q17. Why do units matter?

Answer: Units tell what a value measures and prevent incompatible quantities from being mixed.

Q18. When should you round?

Answer: Usually round near the end unless the question specifically asks for earlier rounding.

Q19. How can you check an answer?

Answer: Use an inverse operation, substitution, estimation, a graph, or a second method.

Q20. What should you identify first in a word problem?

Answer: Identify what is known, what is unknown, and the mathematical relationship connecting them.

Q21. What makes a final answer complete?

Answer: Give the value, correct units when needed, and a brief interpretation in context.

Q22. What should you do if an answer seems unreasonable?

Answer: Re-read the question and check copied values, signs, units, formulas, and calculations.

Q23. Why are diagrams useful?

Answer: A labelled diagram can reveal relationships among lengths, angles, areas, and coordinates.

Q24. Why are tables useful?

Answer: Tables organize values and help reveal patterns, rates, relationships, and missing information.

Q25. Why should you explain your reasoning?

Answer: Reasoning shows why a method works, not just what answer was obtained.

Q26. How do mistakes help learning?

Answer: Analyzing a mistake identifies the misunderstood rule or step and helps prevent repetition.

Q27. When is a calculator useful?

Answer: A calculator helps with lengthy arithmetic after the mathematical setup is understood and estimated.

Q28. Why compare more than one strategy?

Answer: Different strategies may make a problem easier and provide a way to verify the result.

Q29. What is mathematical communication?

Answer: It is presenting ideas clearly with words, symbols, diagrams, tables, graphs, and justified steps.

Q30. What is mathematical modelling?

Answer: It is representing a real situation with mathematics, testing the model, and revising it if needed.