Chapter 36: Data Collection and Sampling
Learn Grade 7 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Data Collection and Sampling with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.
Key Technical Terms
- Population (the entire group being studied)
- Sample (a smaller group selected from a population)
- Bias (an influence that can make results unrepresentative)
- Estimate (a close approximation used to check whether an answer is reasonable)
- Solution (a value or result that satisfies the problem)
- Representation (a way to show mathematics using symbols, diagrams, tables, graphs, or words)
- Reasonableness (whether an answer makes sense in the context of the problem)
How to Learn This Chapter
Read the explanation first, follow the examples one step at a time, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.
36.1 Data
Data are observations, measurements, or categories collected to answer questions. This topic focuses on Data .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Favourite school subject
- Classify it as categorical/qualitative data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Data .
Answer: Use a frequency table
Worked Example 2
Problem: Student heights
- Classify it as quantitative continuous data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Data .
Answer: Measure in centimetres
Worked Example 3
Problem: Number of siblings
- Classify it as quantitative discrete data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Data .
Answer: Count whole numbers
Worked Example 4
Problem: Survey every 10th student
- Classify it as systematic sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Data .
Answer: Check that the list order does not create bias
Worked Example 5
Problem: Survey only basketball team members about school sports
- Classify it as biased sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Data .
Answer: Broaden the sample
Worked Example 6
Problem: Classify the data [4, 6, 8].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 7
Problem: Classify the data [5, 9, 10, 12].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 8
Problem: Classify the data [3, 7, 7, 11].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 9
Problem: Classify the data [20, 25, 30].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 10
Problem: Classify the data [6, 8, 9, 12, 15].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Practice Exercise
Create one new question about Data. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
36.2 Qualitative data
Data are observations, measurements, or categories collected to answer questions. This topic focuses on Qualitative data .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Favourite school subject
- Classify it as categorical/qualitative data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Qualitative data .
Answer: Use a frequency table
Worked Example 2
Problem: Student heights
- Classify it as quantitative continuous data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Qualitative data .
Answer: Measure in centimetres
Worked Example 3
Problem: Number of siblings
- Classify it as quantitative discrete data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Qualitative data .
Answer: Count whole numbers
Worked Example 4
Problem: Survey every 10th student
- Classify it as systematic sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Qualitative data .
Answer: Check that the list order does not create bias
Worked Example 5
Problem: Survey only basketball team members about school sports
- Classify it as biased sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Qualitative data .
Answer: Broaden the sample
Worked Example 6
Problem: Classify the data [4, 6, 8].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 7
Problem: Classify the data [5, 9, 10, 12].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 8
Problem: Classify the data [3, 7, 7, 11].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 9
Problem: Classify the data [20, 25, 30].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 10
Problem: Classify the data [6, 8, 9, 12, 15].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Practice Exercise
Create one new question about Qualitative data. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
36.3 Quantitative data
Data are observations, measurements, or categories collected to answer questions. This topic focuses on Quantitative data .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Favourite school subject
- Classify it as categorical/qualitative data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Quantitative data .
Answer: Use a frequency table
Worked Example 2
Problem: Student heights
- Classify it as quantitative continuous data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Quantitative data .
Answer: Measure in centimetres
Worked Example 3
Problem: Number of siblings
- Classify it as quantitative discrete data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Quantitative data .
Answer: Count whole numbers
Worked Example 4
Problem: Survey every 10th student
- Classify it as systematic sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Quantitative data .
Answer: Check that the list order does not create bias
Worked Example 5
Problem: Survey only basketball team members about school sports
- Classify it as biased sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Quantitative data .
Answer: Broaden the sample
Worked Example 6
Problem: Classify the data [4, 6, 8].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 7
Problem: Classify the data [5, 9, 10, 12].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 8
Problem: Classify the data [3, 7, 7, 11].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 9
Problem: Classify the data [20, 25, 30].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 10
Problem: Classify the data [6, 8, 9, 12, 15].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Practice Exercise
Create one new question about Quantitative data. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
36.4 Discrete data
Data are observations, measurements, or categories collected to answer questions. This topic focuses on Discrete data .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Favourite school subject
- Classify it as categorical/qualitative data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Discrete data .
Answer: Use a frequency table
Worked Example 2
Problem: Student heights
- Classify it as quantitative continuous data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Discrete data .
Answer: Measure in centimetres
Worked Example 3
Problem: Number of siblings
- Classify it as quantitative discrete data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Discrete data .
Answer: Count whole numbers
Worked Example 4
Problem: Survey every 10th student
- Classify it as systematic sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Discrete data .
Answer: Check that the list order does not create bias
Worked Example 5
Problem: Survey only basketball team members about school sports
- Classify it as biased sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Discrete data .
Answer: Broaden the sample
Worked Example 6
Problem: Classify the data [4, 6, 8].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 7
Problem: Classify the data [5, 9, 10, 12].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 8
Problem: Classify the data [3, 7, 7, 11].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 9
Problem: Classify the data [20, 25, 30].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 10
Problem: Classify the data [6, 8, 9, 12, 15].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Practice Exercise
Create one new question about Discrete data. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
36.5 Continuous data
Data are observations, measurements, or categories collected to answer questions. This topic focuses on Continuous data .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Favourite school subject
- Classify it as categorical/qualitative data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Continuous data .
Answer: Use a frequency table
Worked Example 2
Problem: Student heights
- Classify it as quantitative continuous data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Continuous data .
Answer: Measure in centimetres
Worked Example 3
Problem: Number of siblings
- Classify it as quantitative discrete data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Continuous data .
Answer: Count whole numbers
Worked Example 4
Problem: Survey every 10th student
- Classify it as systematic sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Continuous data .
Answer: Check that the list order does not create bias
Worked Example 5
Problem: Survey only basketball team members about school sports
- Classify it as biased sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Continuous data .
Answer: Broaden the sample
Worked Example 6
Problem: Classify the data [4, 6, 8].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 7
Problem: Classify the data [5, 9, 10, 12].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 8
Problem: Classify the data [3, 7, 7, 11].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 9
Problem: Classify the data [20, 25, 30].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 10
Problem: Classify the data [6, 8, 9, 12, 15].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Practice Exercise
Create one new question about Continuous data. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
36.6 Primary data
Data are observations, measurements, or categories collected to answer questions. This topic focuses on Primary data .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Favourite school subject
- Classify it as categorical/qualitative data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Primary data .
Answer: Use a frequency table
Worked Example 2
Problem: Student heights
- Classify it as quantitative continuous data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Primary data .
Answer: Measure in centimetres
Worked Example 3
Problem: Number of siblings
- Classify it as quantitative discrete data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Primary data .
Answer: Count whole numbers
Worked Example 4
Problem: Survey every 10th student
- Classify it as systematic sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Primary data .
Answer: Check that the list order does not create bias
Worked Example 5
Problem: Survey only basketball team members about school sports
- Classify it as biased sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Primary data .
Answer: Broaden the sample
Worked Example 6
Problem: Classify the data [4, 6, 8].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 7
Problem: Classify the data [5, 9, 10, 12].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 8
Problem: Classify the data [3, 7, 7, 11].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 9
Problem: Classify the data [20, 25, 30].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 10
Problem: Classify the data [6, 8, 9, 12, 15].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Practice Exercise
Create one new question about Primary data. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
36.7 Secondary data
Data are observations, measurements, or categories collected to answer questions. This topic focuses on Secondary data .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Favourite school subject
- Classify it as categorical/qualitative data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Secondary data .
Answer: Use a frequency table
Worked Example 2
Problem: Student heights
- Classify it as quantitative continuous data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Secondary data .
Answer: Measure in centimetres
Worked Example 3
Problem: Number of siblings
- Classify it as quantitative discrete data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Secondary data .
Answer: Count whole numbers
Worked Example 4
Problem: Survey every 10th student
- Classify it as systematic sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Secondary data .
Answer: Check that the list order does not create bias
Worked Example 5
Problem: Survey only basketball team members about school sports
- Classify it as biased sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Secondary data .
Answer: Broaden the sample
Worked Example 6
Problem: Classify the data [4, 6, 8].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 7
Problem: Classify the data [5, 9, 10, 12].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 8
Problem: Classify the data [3, 7, 7, 11].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 9
Problem: Classify the data [20, 25, 30].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 10
Problem: Classify the data [6, 8, 9, 12, 15].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Practice Exercise
Create one new question about Secondary data. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
36.8 Population
A population is the entire group being studied. This topic focuses on Population .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Favourite school subject
- Classify it as categorical/qualitative data.
- Choose an appropriate collection/organization method.
Very beginner explanation: A population is the entire group being studied. This topic focuses on Population .
Answer: Use a frequency table
Worked Example 2
Problem: Student heights
- Classify it as quantitative continuous data.
- Choose an appropriate collection/organization method.
Very beginner explanation: A population is the entire group being studied. This topic focuses on Population .
Answer: Measure in centimetres
Worked Example 3
Problem: Number of siblings
- Classify it as quantitative discrete data.
- Choose an appropriate collection/organization method.
Very beginner explanation: A population is the entire group being studied. This topic focuses on Population .
Answer: Count whole numbers
Worked Example 4
Problem: Survey every 10th student
- Classify it as systematic sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: A population is the entire group being studied. This topic focuses on Population .
Answer: Check that the list order does not create bias
Worked Example 5
Problem: Survey only basketball team members about school sports
- Classify it as biased sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: A population is the entire group being studied. This topic focuses on Population .
Answer: Broaden the sample
Worked Example 6
Problem: Classify the data [4, 6, 8].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 7
Problem: Classify the data [5, 9, 10, 12].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 8
Problem: Classify the data [3, 7, 7, 11].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 9
Problem: Classify the data [20, 25, 30].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 10
Problem: Classify the data [6, 8, 9, 12, 15].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Practice Exercise
Create one new question about Population. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
36.9 Sample
A sample is a smaller group selected from a population. This topic focuses on Sample .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Favourite school subject
- Classify it as categorical/qualitative data.
- Choose an appropriate collection/organization method.
Very beginner explanation: A sample is a smaller group selected from a population. This topic focuses on Sample .
Answer: Use a frequency table
Worked Example 2
Problem: Student heights
- Classify it as quantitative continuous data.
- Choose an appropriate collection/organization method.
Very beginner explanation: A sample is a smaller group selected from a population. This topic focuses on Sample .
Answer: Measure in centimetres
Worked Example 3
Problem: Number of siblings
- Classify it as quantitative discrete data.
- Choose an appropriate collection/organization method.
Very beginner explanation: A sample is a smaller group selected from a population. This topic focuses on Sample .
Answer: Count whole numbers
Worked Example 4
Problem: Survey every 10th student
- Classify it as systematic sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: A sample is a smaller group selected from a population. This topic focuses on Sample .
Answer: Check that the list order does not create bias
Worked Example 5
Problem: Survey only basketball team members about school sports
- Classify it as biased sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: A sample is a smaller group selected from a population. This topic focuses on Sample .
Answer: Broaden the sample
Worked Example 6
Problem: Classify the data [4, 6, 8].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 7
Problem: Classify the data [5, 9, 10, 12].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 8
Problem: Classify the data [3, 7, 7, 11].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 9
Problem: Classify the data [20, 25, 30].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 10
Problem: Classify the data [6, 8, 9, 12, 15].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Practice Exercise
Create one new question about Sample. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
36.10 Representative sample
A sample is a smaller group selected from a population. This topic focuses on Representative sample .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Favourite school subject
- Classify it as categorical/qualitative data.
- Choose an appropriate collection/organization method.
Very beginner explanation: A sample is a smaller group selected from a population. This topic focuses on Representative sample .
Answer: Use a frequency table
Worked Example 2
Problem: Student heights
- Classify it as quantitative continuous data.
- Choose an appropriate collection/organization method.
Very beginner explanation: A sample is a smaller group selected from a population. This topic focuses on Representative sample .
Answer: Measure in centimetres
Worked Example 3
Problem: Number of siblings
- Classify it as quantitative discrete data.
- Choose an appropriate collection/organization method.
Very beginner explanation: A sample is a smaller group selected from a population. This topic focuses on Representative sample .
Answer: Count whole numbers
Worked Example 4
Problem: Survey every 10th student
- Classify it as systematic sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: A sample is a smaller group selected from a population. This topic focuses on Representative sample .
Answer: Check that the list order does not create bias
Worked Example 5
Problem: Survey only basketball team members about school sports
- Classify it as biased sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: A sample is a smaller group selected from a population. This topic focuses on Representative sample .
Answer: Broaden the sample
Worked Example 6
Problem: Classify the data [4, 6, 8].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 7
Problem: Classify the data [5, 9, 10, 12].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 8
Problem: Classify the data [3, 7, 7, 11].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 9
Problem: Classify the data [20, 25, 30].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 10
Problem: Classify the data [6, 8, 9, 12, 15].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Practice Exercise
Create one new question about Representative sample. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
36.11 Random sampling
Random sampling is an important Grade 7 idea in Data Collection and Sampling. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Favourite school subject
- Classify it as categorical/qualitative data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Random sampling is an important Grade 7 idea in Data Collection and Sampling. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Use a frequency table
Worked Example 2
Problem: Student heights
- Classify it as quantitative continuous data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Random sampling is an important Grade 7 idea in Data Collection and Sampling. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Measure in centimetres
Worked Example 3
Problem: Number of siblings
- Classify it as quantitative discrete data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Random sampling is an important Grade 7 idea in Data Collection and Sampling. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Count whole numbers
Worked Example 4
Problem: Survey every 10th student
- Classify it as systematic sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Random sampling is an important Grade 7 idea in Data Collection and Sampling. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Check that the list order does not create bias
Worked Example 5
Problem: Survey only basketball team members about school sports
- Classify it as biased sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Random sampling is an important Grade 7 idea in Data Collection and Sampling. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Broaden the sample
Worked Example 6
Problem: Classify the data [4, 6, 8].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 7
Problem: Classify the data [5, 9, 10, 12].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 8
Problem: Classify the data [3, 7, 7, 11].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 9
Problem: Classify the data [20, 25, 30].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 10
Problem: Classify the data [6, 8, 9, 12, 15].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Practice Exercise
Create one new question about Random sampling. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
36.12 Systematic sampling
Systematic sampling is an important Grade 7 idea in Data Collection and Sampling. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Favourite school subject
- Classify it as categorical/qualitative data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Systematic sampling is an important Grade 7 idea in Data Collection and Sampling. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Use a frequency table
Worked Example 2
Problem: Student heights
- Classify it as quantitative continuous data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Systematic sampling is an important Grade 7 idea in Data Collection and Sampling. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Measure in centimetres
Worked Example 3
Problem: Number of siblings
- Classify it as quantitative discrete data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Systematic sampling is an important Grade 7 idea in Data Collection and Sampling. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Count whole numbers
Worked Example 4
Problem: Survey every 10th student
- Classify it as systematic sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Systematic sampling is an important Grade 7 idea in Data Collection and Sampling. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Check that the list order does not create bias
Worked Example 5
Problem: Survey only basketball team members about school sports
- Classify it as biased sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Systematic sampling is an important Grade 7 idea in Data Collection and Sampling. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Broaden the sample
Worked Example 6
Problem: Classify the data [4, 6, 8].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 7
Problem: Classify the data [5, 9, 10, 12].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 8
Problem: Classify the data [3, 7, 7, 11].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 9
Problem: Classify the data [20, 25, 30].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 10
Problem: Classify the data [6, 8, 9, 12, 15].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Practice Exercise
Create one new question about Systematic sampling. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
36.13 Sampling bias
Bias is an influence that can make data collection or conclusions unrepresentative. This topic focuses on Sampling bias .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Favourite school subject
- Classify it as categorical/qualitative data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Bias is an influence that can make data collection or conclusions unrepresentative. This topic focuses on Sampling bias .
Answer: Use a frequency table
Worked Example 2
Problem: Student heights
- Classify it as quantitative continuous data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Bias is an influence that can make data collection or conclusions unrepresentative. This topic focuses on Sampling bias .
Answer: Measure in centimetres
Worked Example 3
Problem: Number of siblings
- Classify it as quantitative discrete data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Bias is an influence that can make data collection or conclusions unrepresentative. This topic focuses on Sampling bias .
Answer: Count whole numbers
Worked Example 4
Problem: Survey every 10th student
- Classify it as systematic sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Bias is an influence that can make data collection or conclusions unrepresentative. This topic focuses on Sampling bias .
Answer: Check that the list order does not create bias
Worked Example 5
Problem: Survey only basketball team members about school sports
- Classify it as biased sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Bias is an influence that can make data collection or conclusions unrepresentative. This topic focuses on Sampling bias .
Answer: Broaden the sample
Worked Example 6
Problem: Classify the data [4, 6, 8].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 7
Problem: Classify the data [5, 9, 10, 12].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 8
Problem: Classify the data [3, 7, 7, 11].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 9
Problem: Classify the data [20, 25, 30].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 10
Problem: Classify the data [6, 8, 9, 12, 15].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Practice Exercise
Create one new question about Sampling bias. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
36.14 Designing survey questions
Designing survey questions is an important Grade 7 idea in Data Collection and Sampling. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Favourite school subject
- Classify it as categorical/qualitative data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Designing survey questions is an important Grade 7 idea in Data Collection and Sampling. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Use a frequency table
Worked Example 2
Problem: Student heights
- Classify it as quantitative continuous data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Designing survey questions is an important Grade 7 idea in Data Collection and Sampling. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Measure in centimetres
Worked Example 3
Problem: Number of siblings
- Classify it as quantitative discrete data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Designing survey questions is an important Grade 7 idea in Data Collection and Sampling. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Count whole numbers
Worked Example 4
Problem: Survey every 10th student
- Classify it as systematic sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Designing survey questions is an important Grade 7 idea in Data Collection and Sampling. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Check that the list order does not create bias
Worked Example 5
Problem: Survey only basketball team members about school sports
- Classify it as biased sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Designing survey questions is an important Grade 7 idea in Data Collection and Sampling. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Broaden the sample
Worked Example 6
Problem: Explain Designing survey questions in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Designing survey questions becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Designing survey questions and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Designing survey questions becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Designing survey questions using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Designing survey questions becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Designing survey questions problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Designing survey questions becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Designing survey questions could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Designing survey questions becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Designing survey questions. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
36.15 Ethical data collection
Data are observations, measurements, or categories collected to answer questions. This topic focuses on Ethical data collection .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Favourite school subject
- Classify it as categorical/qualitative data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Ethical data collection .
Answer: Use a frequency table
Worked Example 2
Problem: Student heights
- Classify it as quantitative continuous data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Ethical data collection .
Answer: Measure in centimetres
Worked Example 3
Problem: Number of siblings
- Classify it as quantitative discrete data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Ethical data collection .
Answer: Count whole numbers
Worked Example 4
Problem: Survey every 10th student
- Classify it as systematic sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Ethical data collection .
Answer: Check that the list order does not create bias
Worked Example 5
Problem: Survey only basketball team members about school sports
- Classify it as biased sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Ethical data collection .
Answer: Broaden the sample
Worked Example 6
Problem: Classify the data [4, 6, 8].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 7
Problem: Classify the data [5, 9, 10, 12].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 8
Problem: Classify the data [3, 7, 7, 11].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 9
Problem: Classify the data [20, 25, 30].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 10
Problem: Classify the data [6, 8, 9, 12, 15].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Practice Exercise
Create one new question about Ethical data collection. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
Chapter Notes, Practice, and Common Mistakes
Chapter Notes
- Read the complete question before choosing an operation, formula, graph, or model.
- Write technical words together with their meaning until you are comfortable using them.
- Show all important steps so another student can follow your reasoning.
- Keep units, labels, signs, axes, variables, and mathematical symbols clear.
- Estimate before or after calculating when an estimate can help check reasonableness.
- For real-life problems, explain what the final number means in the situation.
Extra Practice
- Create and solve a new question about Data . Show your reasoning and check your answer.
- Create and solve a new question about Qualitative data . Show your reasoning and check your answer.
- Create and solve a new question about Quantitative data . Show your reasoning and check your answer.
- Create and solve a new question about Discrete data . Show your reasoning and check your answer.
- Create and solve a new question about Continuous data . Show your reasoning and check your answer.
- Create and solve a new question about Primary data . Show your reasoning and check your answer.
- Create and solve a new question about Secondary data . Show your reasoning and check your answer.
- Create and solve a new question about Population . Show your reasoning and check your answer.
- Create and solve a new question about Sample . Show your reasoning and check your answer.
- Create and solve a new question about Representative sample . Show your reasoning and check your answer.
- Create and solve a new question about Random sampling . Show your reasoning and check your answer.
- Create and solve a new question about Systematic sampling . Show your reasoning and check your answer.
Common Mistakes
- Using a biased or unrepresentative sample.
- Reading graph scales incorrectly.
- Treating a misleading graph as trustworthy without checking the axes.
- Assuming dependent events are independent.
- Using percentages in a circle graph that do not total 100%.
30 Review Questions and Answers
Q1. What is important to remember about Data?
Answer: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Data.
Q2. What is important to remember about Qualitative data?
Answer: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Qualitative data.
Q3. What is important to remember about Quantitative data?
Answer: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Quantitative data.
Q4. What is important to remember about Discrete data?
Answer: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Discrete data.
Q5. What is important to remember about Continuous data?
Answer: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Continuous data.
Q6. What is important to remember about Primary data?
Answer: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Primary data.
Q7. What is important to remember about Secondary data?
Answer: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Secondary data.
Q8. What is important to remember about Population?
Answer: A population is the entire group being studied. This topic focuses on Population.
Q9. What is important to remember about Sample?
Answer: A sample is a smaller group selected from a population. This topic focuses on Sample.
Q10. What is important to remember about Representative sample?
Answer: A sample is a smaller group selected from a population. This topic focuses on Representative sample.
Q11. What is important to remember about Random sampling?
Answer: Random sampling is an important Grade 7 idea in Data Collection and Sampling. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q12. What is important to remember about Systematic sampling?
Answer: Systematic sampling is an important Grade 7 idea in Data Collection and Sampling. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q13. What is important to remember about Sampling bias?
Answer: Bias is an influence that can make data collection or conclusions unrepresentative. This topic focuses on Sampling bias.
Q14. What is important to remember about Designing survey questions?
Answer: Designing survey questions is an important Grade 7 idea in Data Collection and Sampling. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q15. What is important to remember about Ethical data collection?
Answer: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Ethical data collection.
Q16. Why should you show your steps?
Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.
Q17. Why is estimation useful?
Answer: Estimation helps you judge whether a final answer is reasonable before accepting it.
Q18. Why do units matter?
Answer: Units tell what a value measures and prevent incompatible quantities from being mixed.
Q19. When should you round?
Answer: Usually round near the end of a calculation unless the question specifically asks for earlier rounding.
Q20. How can you check an answer?
Answer: Use an inverse operation, substitution, estimation, a graph, or a second method.
Q21. What should you identify first in a word problem?
Answer: Identify what is known, what is unknown, and the relationship connecting them.
Q22. What makes a final answer complete?
Answer: Give the value, correct units when needed, and a brief interpretation in context.
Q23. What should you do if an answer seems unreasonable?
Answer: Re-read the question, check copied values, signs, units, formulas, and calculations.
Q24. Why are diagrams useful?
Answer: A labelled diagram can reveal relationships between lengths, angles, areas, and other quantities.
Q25. Why are tables useful?
Answer: Tables organize values and help reveal patterns, relationships, rates, and missing information.
Q26. Why should you explain your reasoning?
Answer: Reasoning shows why a method works, not just what answer you obtained.
Q27. How do mistakes help learning?
Answer: Analyzing a mistake identifies the misunderstood rule or step and helps prevent the same error later.
Q28. How should you study this chapter?
Answer: Review definitions, redo worked examples without looking, practise mixed questions, and explain solutions in your own words.
Q29. When is a calculator useful?
Answer: A calculator is useful for lengthy arithmetic after you understand the mathematical setup and can estimate the expected size of the answer.
Q30. Why compare more than one strategy?
Answer: Different strategies can make a problem easier and provide a way to verify the result.