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Chapter 38: Measures of Central Tendency

Learn Grade 6 mathematics with very-beginner explanations, original worked examples, practice, reasoning, and review.

Grade 6Beginner Friendly10 Examples Per Topic30 Q&APractice + Review
Estimated reading time0% read
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Chapter Overview

This chapter teaches Measures of Central Tendency in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.

Key Technical Terms

  • Mean (The mean is found by adding all values and dividing by the number of values.)
  • Median (The median is the middle value after data are ordered.)
  • Mode (The mode is the value that appears most often.)
  • Choosing a useful measure (Choosing a useful measure is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Interpreting averages (Interpreting averages is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Real-life average problems (Real-life average problems is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)

How to Learn This Chapter

Read the explanation first, follow each worked example slowly, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.

38.1 Mean

The mean is found by adding all values and dividing by the number of values. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find the mean of [4, 6, 8, 10].

  1. Add the values to get 28.
  2. Divide by 4.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 7

Worked Example 2

Problem: Find the mean of [5, 7, 7, 9, 12].

  1. Add the values to get 40.
  2. Divide by 5.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 8

Worked Example 3

Problem: Find the mean of [3, 5, 8, 8, 11].

  1. Add the values to get 35.
  2. Divide by 5.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 7

Worked Example 4

Problem: Find the mean of [10, 12, 14, 16].

  1. Add the values to get 52.
  2. Divide by 4.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 13

Worked Example 5

Problem: Find the mean of [2, 4, 6, 8, 10].

  1. Add the values to get 30.
  2. Divide by 5.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 6

Worked Example 6

Problem: Find the mean of [1, 5, 5, 6, 13].

  1. Add the values to get 30.
  2. Divide by 5.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 6

Worked Example 7

Problem: Find the mean of [20, 25, 25, 30].

  1. Add the values to get 100.
  2. Divide by 4.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 25

Worked Example 8

Problem: Find the mean of [7, 8, 9, 10, 11].

  1. Add the values to get 45.
  2. Divide by 5.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 9

Worked Example 9

Problem: Find the mean of [3, 3, 4, 5, 9].

  1. Add the values to get 24.
  2. Divide by 5.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 4.8

Worked Example 10

Problem: Find the mean of [12, 15, 18, 21].

  1. Add the values to get 66.
  2. Divide by 4.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 16.5

Practice Exercise

Create one new Grade 6 problem about Mean. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

38.2 Median

The median is the middle value after data are ordered. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find the median of [4, 6, 8, 10].

  1. Order the data.
  2. Find the middle value or average the two middle values.

Very beginner explanation: The median is based on position after ordering.

Answer: 7

Worked Example 2

Problem: Find the median of [5, 7, 7, 9, 12].

  1. Order the data.
  2. Find the middle value or average the two middle values.

Very beginner explanation: The median is based on position after ordering.

Answer: 7

Worked Example 3

Problem: Find the median of [3, 5, 8, 8, 11].

  1. Order the data.
  2. Find the middle value or average the two middle values.

Very beginner explanation: The median is based on position after ordering.

Answer: 8

Worked Example 4

Problem: Find the median of [10, 12, 14, 16].

  1. Order the data.
  2. Find the middle value or average the two middle values.

Very beginner explanation: The median is based on position after ordering.

Answer: 13

Worked Example 5

Problem: Find the median of [2, 4, 6, 8, 10].

  1. Order the data.
  2. Find the middle value or average the two middle values.

Very beginner explanation: The median is based on position after ordering.

Answer: 6

Worked Example 6

Problem: Find the median of [1, 5, 5, 6, 13].

  1. Order the data.
  2. Find the middle value or average the two middle values.

Very beginner explanation: The median is based on position after ordering.

Answer: 5

Worked Example 7

Problem: Find the median of [20, 25, 25, 30].

  1. Order the data.
  2. Find the middle value or average the two middle values.

Very beginner explanation: The median is based on position after ordering.

Answer: 25

Worked Example 8

Problem: Find the median of [7, 8, 9, 10, 11].

  1. Order the data.
  2. Find the middle value or average the two middle values.

Very beginner explanation: The median is based on position after ordering.

Answer: 9

Worked Example 9

Problem: Find the median of [3, 3, 4, 5, 9].

  1. Order the data.
  2. Find the middle value or average the two middle values.

Very beginner explanation: The median is based on position after ordering.

Answer: 4

Worked Example 10

Problem: Find the median of [12, 15, 18, 21].

  1. Order the data.
  2. Find the middle value or average the two middle values.

Very beginner explanation: The median is based on position after ordering.

Answer: 16.5

Practice Exercise

Create one new Grade 6 problem about Median. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

38.3 Mode

The mode is the value that appears most often. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find the mode of [4, 6, 8, 10].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: No mode

Worked Example 2

Problem: Find the mode of [5, 7, 7, 9, 12].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: 7

Worked Example 3

Problem: Find the mode of [3, 5, 8, 8, 11].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: 8

Worked Example 4

Problem: Find the mode of [10, 12, 14, 16].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: No mode

Worked Example 5

Problem: Find the mode of [2, 4, 6, 8, 10].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: No mode

Worked Example 6

Problem: Find the mode of [1, 5, 5, 6, 13].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: 5

Worked Example 7

Problem: Find the mode of [20, 25, 25, 30].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: 25

Worked Example 8

Problem: Find the mode of [7, 8, 9, 10, 11].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: No mode

Worked Example 9

Problem: Find the mode of [3, 3, 4, 5, 9].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: 3

Worked Example 10

Problem: Find the mode of [12, 15, 18, 21].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: No mode

Practice Exercise

Create one new Grade 6 problem about Mode. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

38.4 Finding the mean

The mean is found by adding all values and dividing by the number of values. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find the mean of [4, 6, 8, 10].

  1. Add the values to get 28.
  2. Divide by 4.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 7

Worked Example 2

Problem: Find the mean of [5, 7, 7, 9, 12].

  1. Add the values to get 40.
  2. Divide by 5.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 8

Worked Example 3

Problem: Find the mean of [3, 5, 8, 8, 11].

  1. Add the values to get 35.
  2. Divide by 5.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 7

Worked Example 4

Problem: Find the mean of [10, 12, 14, 16].

  1. Add the values to get 52.
  2. Divide by 4.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 13

Worked Example 5

Problem: Find the mean of [2, 4, 6, 8, 10].

  1. Add the values to get 30.
  2. Divide by 5.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 6

Worked Example 6

Problem: Find the mean of [1, 5, 5, 6, 13].

  1. Add the values to get 30.
  2. Divide by 5.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 6

Worked Example 7

Problem: Find the mean of [20, 25, 25, 30].

  1. Add the values to get 100.
  2. Divide by 4.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 25

Worked Example 8

Problem: Find the mean of [7, 8, 9, 10, 11].

  1. Add the values to get 45.
  2. Divide by 5.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 9

Worked Example 9

Problem: Find the mean of [3, 3, 4, 5, 9].

  1. Add the values to get 24.
  2. Divide by 5.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 4.8

Worked Example 10

Problem: Find the mean of [12, 15, 18, 21].

  1. Add the values to get 66.
  2. Divide by 4.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 16.5

Practice Exercise

Create one new Grade 6 problem about Finding the mean. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

38.5 Finding the median

The median is the middle value after data are ordered. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find the median of [4, 6, 8, 10].

  1. Order the data.
  2. Find the middle value or average the two middle values.

Very beginner explanation: The median is based on position after ordering.

Answer: 7

Worked Example 2

Problem: Find the median of [5, 7, 7, 9, 12].

  1. Order the data.
  2. Find the middle value or average the two middle values.

Very beginner explanation: The median is based on position after ordering.

Answer: 7

Worked Example 3

Problem: Find the median of [3, 5, 8, 8, 11].

  1. Order the data.
  2. Find the middle value or average the two middle values.

Very beginner explanation: The median is based on position after ordering.

Answer: 8

Worked Example 4

Problem: Find the median of [10, 12, 14, 16].

  1. Order the data.
  2. Find the middle value or average the two middle values.

Very beginner explanation: The median is based on position after ordering.

Answer: 13

Worked Example 5

Problem: Find the median of [2, 4, 6, 8, 10].

  1. Order the data.
  2. Find the middle value or average the two middle values.

Very beginner explanation: The median is based on position after ordering.

Answer: 6

Worked Example 6

Problem: Find the median of [1, 5, 5, 6, 13].

  1. Order the data.
  2. Find the middle value or average the two middle values.

Very beginner explanation: The median is based on position after ordering.

Answer: 5

Worked Example 7

Problem: Find the median of [20, 25, 25, 30].

  1. Order the data.
  2. Find the middle value or average the two middle values.

Very beginner explanation: The median is based on position after ordering.

Answer: 25

Worked Example 8

Problem: Find the median of [7, 8, 9, 10, 11].

  1. Order the data.
  2. Find the middle value or average the two middle values.

Very beginner explanation: The median is based on position after ordering.

Answer: 9

Worked Example 9

Problem: Find the median of [3, 3, 4, 5, 9].

  1. Order the data.
  2. Find the middle value or average the two middle values.

Very beginner explanation: The median is based on position after ordering.

Answer: 4

Worked Example 10

Problem: Find the median of [12, 15, 18, 21].

  1. Order the data.
  2. Find the middle value or average the two middle values.

Very beginner explanation: The median is based on position after ordering.

Answer: 16.5

Practice Exercise

Create one new Grade 6 problem about Finding the median. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

38.6 Finding the mode

The mode is the value that appears most often. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find the mode of [4, 6, 8, 10].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: No mode

Worked Example 2

Problem: Find the mode of [5, 7, 7, 9, 12].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: 7

Worked Example 3

Problem: Find the mode of [3, 5, 8, 8, 11].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: 8

Worked Example 4

Problem: Find the mode of [10, 12, 14, 16].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: No mode

Worked Example 5

Problem: Find the mode of [2, 4, 6, 8, 10].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: No mode

Worked Example 6

Problem: Find the mode of [1, 5, 5, 6, 13].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: 5

Worked Example 7

Problem: Find the mode of [20, 25, 25, 30].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: 25

Worked Example 8

Problem: Find the mode of [7, 8, 9, 10, 11].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: No mode

Worked Example 9

Problem: Find the mode of [3, 3, 4, 5, 9].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: 3

Worked Example 10

Problem: Find the mode of [12, 15, 18, 21].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: No mode

Practice Exercise

Create one new Grade 6 problem about Finding the mode. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

38.7 Data sets with no mode

The mode is the value that appears most often. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find the mode of [4, 6, 8, 10].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: No mode

Worked Example 2

Problem: Find the mode of [5, 7, 7, 9, 12].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: 7

Worked Example 3

Problem: Find the mode of [3, 5, 8, 8, 11].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: 8

Worked Example 4

Problem: Find the mode of [10, 12, 14, 16].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: No mode

Worked Example 5

Problem: Find the mode of [2, 4, 6, 8, 10].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: No mode

Worked Example 6

Problem: Find the mode of [1, 5, 5, 6, 13].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: 5

Worked Example 7

Problem: Find the mode of [20, 25, 25, 30].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: 25

Worked Example 8

Problem: Find the mode of [7, 8, 9, 10, 11].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: No mode

Worked Example 9

Problem: Find the mode of [3, 3, 4, 5, 9].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: 3

Worked Example 10

Problem: Find the mode of [12, 15, 18, 21].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: No mode

Practice Exercise

Create one new Grade 6 problem about Data sets with no mode. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

38.8 Data sets with more than one mode

The mode is the value that appears most often. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find the mode of [4, 6, 8, 10].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: No mode

Worked Example 2

Problem: Find the mode of [5, 7, 7, 9, 12].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: 7

Worked Example 3

Problem: Find the mode of [3, 5, 8, 8, 11].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: 8

Worked Example 4

Problem: Find the mode of [10, 12, 14, 16].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: No mode

Worked Example 5

Problem: Find the mode of [2, 4, 6, 8, 10].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: No mode

Worked Example 6

Problem: Find the mode of [1, 5, 5, 6, 13].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: 5

Worked Example 7

Problem: Find the mode of [20, 25, 25, 30].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: 25

Worked Example 8

Problem: Find the mode of [7, 8, 9, 10, 11].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: No mode

Worked Example 9

Problem: Find the mode of [3, 3, 4, 5, 9].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: 3

Worked Example 10

Problem: Find the mode of [12, 15, 18, 21].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: No mode

Practice Exercise

Create one new Grade 6 problem about Data sets with more than one mode. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

38.9 Effect of an outlier on mean

The mean is found by adding all values and dividing by the number of values. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find the mean of [4, 6, 8, 10].

  1. Add the values to get 28.
  2. Divide by 4.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 7

Worked Example 2

Problem: Find the mean of [5, 7, 7, 9, 12].

  1. Add the values to get 40.
  2. Divide by 5.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 8

Worked Example 3

Problem: Find the mean of [3, 5, 8, 8, 11].

  1. Add the values to get 35.
  2. Divide by 5.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 7

Worked Example 4

Problem: Find the mean of [10, 12, 14, 16].

  1. Add the values to get 52.
  2. Divide by 4.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 13

Worked Example 5

Problem: Find the mean of [2, 4, 6, 8, 10].

  1. Add the values to get 30.
  2. Divide by 5.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 6

Worked Example 6

Problem: Find the mean of [1, 5, 5, 6, 13].

  1. Add the values to get 30.
  2. Divide by 5.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 6

Worked Example 7

Problem: Find the mean of [20, 25, 25, 30].

  1. Add the values to get 100.
  2. Divide by 4.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 25

Worked Example 8

Problem: Find the mean of [7, 8, 9, 10, 11].

  1. Add the values to get 45.
  2. Divide by 5.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 9

Worked Example 9

Problem: Find the mean of [3, 3, 4, 5, 9].

  1. Add the values to get 24.
  2. Divide by 5.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 4.8

Worked Example 10

Problem: Find the mean of [12, 15, 18, 21].

  1. Add the values to get 66.
  2. Divide by 4.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 16.5

Practice Exercise

Create one new Grade 6 problem about Effect of an outlier on mean. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

38.10 Choosing a useful measure

Choosing a useful measure is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Use Choosing a useful measure to analyze the values 28 and 13. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Choosing a useful measure is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 2

Problem: Use Choosing a useful measure to analyze the values 12 and 14. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Choosing a useful measure is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 3

Problem: Use Choosing a useful measure to analyze the values 21 and 15. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Choosing a useful measure is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 4

Problem: Use Choosing a useful measure to analyze the values 26 and 18. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Choosing a useful measure is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 5

Problem: Use Choosing a useful measure to analyze the values 11 and 6. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Choosing a useful measure is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 6

Problem: Use Choosing a useful measure to analyze the values 24 and 5. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Choosing a useful measure is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 7

Problem: Use Choosing a useful measure to analyze the values 26 and 5. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Choosing a useful measure is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 8

Problem: Use Choosing a useful measure to analyze the values 27 and 2. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Choosing a useful measure is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 9

Problem: Use Choosing a useful measure to analyze the values 18 and 2. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Choosing a useful measure is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 10

Problem: Use Choosing a useful measure to analyze the values 13 and 14. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Choosing a useful measure is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Practice Exercise

Create one new Grade 6 problem about Choosing a useful measure. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

38.11 Interpreting averages

Interpreting averages is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Use Interpreting averages to analyze the values 24 and 13. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Interpreting averages is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 2

Problem: Use Interpreting averages to analyze the values 21 and 20. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Interpreting averages is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 3

Problem: Use Interpreting averages to analyze the values 28 and 14. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Interpreting averages is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 4

Problem: Use Interpreting averages to analyze the values 29 and 6. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Interpreting averages is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 5

Problem: Use Interpreting averages to analyze the values 5 and 13. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Interpreting averages is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 6

Problem: Use Interpreting averages to analyze the values 27 and 10. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Interpreting averages is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 7

Problem: Use Interpreting averages to analyze the values 5 and 18. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Interpreting averages is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 8

Problem: Use Interpreting averages to analyze the values 9 and 2. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Interpreting averages is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 9

Problem: Use Interpreting averages to analyze the values 12 and 14. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Interpreting averages is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 10

Problem: Use Interpreting averages to analyze the values 22 and 18. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Interpreting averages is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Practice Exercise

Create one new Grade 6 problem about Interpreting averages. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

38.12 Real-life average problems

Real-life average problems is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Use Real-life average problems to analyze the values 27 and 6. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Real-life average problems is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 2

Problem: Use Real-life average problems to analyze the values 14 and 4. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Real-life average problems is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 3

Problem: Use Real-life average problems to analyze the values 10 and 17. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Real-life average problems is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 4

Problem: Use Real-life average problems to analyze the values 8 and 8. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Real-life average problems is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 5

Problem: Use Real-life average problems to analyze the values 8 and 9. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Real-life average problems is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 6

Problem: Use Real-life average problems to analyze the values 26 and 20. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Real-life average problems is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 7

Problem: Use Real-life average problems to analyze the values 11 and 5. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Real-life average problems is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 8

Problem: Use Real-life average problems to analyze the values 16 and 12. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Real-life average problems is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 9

Problem: Use Real-life average problems to analyze the values 10 and 12. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Real-life average problems is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 10

Problem: Use Real-life average problems to analyze the values 8 and 17. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Real-life average problems is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Practice Exercise

Create one new Grade 6 problem about Real-life average problems. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

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30 Review Questions and Answers

Q1. What is important to understand about Mean?

Answer: The mean is found by adding all values and dividing by the number of values.

Q2. What is important to understand about Median?

Answer: The median is the middle value after data are ordered.

Q3. What is important to understand about Mode?

Answer: The mode is the value that appears most often.

Q4. What is important to understand about Finding the mean?

Answer: The mean is found by adding all values and dividing by the number of values.

Q5. What is important to understand about Finding the median?

Answer: The median is the middle value after data are ordered.

Q6. What is important to understand about Finding the mode?

Answer: The mode is the value that appears most often.

Q7. What is important to understand about Data sets with no mode?

Answer: The mode is the value that appears most often.

Q8. What is important to understand about Data sets with more than one mode?

Answer: The mode is the value that appears most often.

Q9. What is important to understand about Effect of an outlier on mean?

Answer: The mean is found by adding all values and dividing by the number of values.

Q10. What is important to understand about Choosing a useful measure?

Answer: Choosing a useful measure is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q11. What is important to understand about Interpreting averages?

Answer: Interpreting averages is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q12. What is important to understand about Real-life average problems?

Answer: Real-life average problems is a Grade 6 mathematics idea in Measures of Central Tendency. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q13. Why should you show your steps?

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

Q14. Why is estimation useful?

Answer: Estimation helps you judge whether a final answer is reasonable before accepting it.

Q15. Why do units matter?

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

Q16. When should you round?

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

Q17. How can you check an answer?

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

Q18. What should you identify first in a word problem?

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

Q19. What makes a final answer complete?

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

Q20. What should you do if an answer seems unreasonable?

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

Q21. Why are diagrams useful?

Answer: A labelled diagram can reveal relationships that are harder to see in words alone.

Q22. Why are tables useful?

Answer: Tables organize values so patterns, rates, comparisons, and missing information are easier to see.

Q23. Why are graphs useful?

Answer: Graphs make relationships, changes, trends, and comparisons visible.

Q24. Why should you explain your reasoning?

Answer: An explanation shows why a method works instead of only giving a final number.

Q25. Why can more than one strategy be correct?

Answer: Different correct strategies can represent the same mathematics in different but equivalent ways.

Q26. What should you do before using a formula or rule?

Answer: Check what each quantity means and whether the rule matches the situation.

Q27. How does practice help in mathematics?

Answer: Practice builds accuracy and fluency while helping you recognize which strategies fit different problems.

Q28. What is a good way to learn from a mistake?

Answer: Find the exact step where the reasoning changed from correct to incorrect, then solve a similar problem again.

Q29. Why should you compare an exact answer with an estimate?

Answer: The estimate gives a quick reasonableness check for the exact calculation.

Q30. What does representing mathematics mean?

Answer: It means showing an idea with numbers, symbols, words, diagrams, tables, graphs, or models.