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Chapter 40: Histograms

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 Histograms in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.

Key Technical Terms

  • Meaning of histogram (The mean is found by adding all values and dividing by the number of values.)
  • Intervals (Intervals is a Grade 6 mathematics idea in Histograms. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Frequency (Frequency is a Grade 6 mathematics idea in Histograms. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Continuous numerical data (Continuous numerical data is a Grade 6 mathematics idea in Histograms. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Choosing interval widths (Choosing interval widths is a Grade 6 mathematics idea in Histograms. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Reading a histogram (A histogram groups numerical data into intervals and shows the frequency in each interval.)

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.

40.1 Meaning of histogram

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 Meaning of histogram. 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.

40.2 Intervals

Intervals is a Grade 6 mathematics idea in Histograms. 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 Intervals to analyze the values 11 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: Intervals is a Grade 6 mathematics idea in Histograms. 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 Intervals to analyze the values 19 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: Intervals is a Grade 6 mathematics idea in Histograms. 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 Intervals to analyze the values 13 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: Intervals is a Grade 6 mathematics idea in Histograms. 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 Intervals to analyze the values 17 and 19. 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: Intervals is a Grade 6 mathematics idea in Histograms. 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 Intervals to analyze the values 3 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: Intervals is a Grade 6 mathematics idea in Histograms. 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 Intervals 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: Intervals is a Grade 6 mathematics idea in Histograms. 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 Intervals to analyze the values 15 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: Intervals is a Grade 6 mathematics idea in Histograms. 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 Intervals to analyze the values 4 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: Intervals is a Grade 6 mathematics idea in Histograms. 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 Intervals to analyze the values 11 and 3. 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: Intervals is a Grade 6 mathematics idea in Histograms. 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 Intervals to analyze the values 12 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: Intervals is a Grade 6 mathematics idea in Histograms. 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 Intervals. 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.

40.3 Frequency

Frequency is a Grade 6 mathematics idea in Histograms. 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 Frequency to analyze the values 17 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: Frequency is a Grade 6 mathematics idea in Histograms. 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 Frequency to analyze the values 18 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: Frequency is a Grade 6 mathematics idea in Histograms. 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 Frequency to analyze the values 30 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: Frequency is a Grade 6 mathematics idea in Histograms. 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 Frequency to analyze the values 30 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: Frequency is a Grade 6 mathematics idea in Histograms. 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 Frequency to analyze the values 14 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: Frequency is a Grade 6 mathematics idea in Histograms. 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 Frequency to analyze the values 8 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: Frequency is a Grade 6 mathematics idea in Histograms. 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 Frequency to analyze the values 3 and 16. 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: Frequency is a Grade 6 mathematics idea in Histograms. 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 Frequency to analyze the values 4 and 11. 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: Frequency is a Grade 6 mathematics idea in Histograms. 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 Frequency to analyze the values 18 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: Frequency is a Grade 6 mathematics idea in Histograms. 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 Frequency to analyze the values 26 and 3. 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: Frequency is a Grade 6 mathematics idea in Histograms. 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 Frequency. 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.

40.4 Continuous numerical data

Continuous numerical data is a Grade 6 mathematics idea in Histograms. 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: Classify the data values [4, 6, 8, 10] as quantitative or qualitative.

  1. They are numerical values.
  2. Numerical counts or measurements are quantitative.

Very beginner explanation: Quantitative data use numbers to represent counts or measurements.

Answer: Quantitative

Worked Example 2

Problem: Classify the data values [5, 7, 7, 9, 12] as quantitative or qualitative.

  1. They are numerical values.
  2. Numerical counts or measurements are quantitative.

Very beginner explanation: Quantitative data use numbers to represent counts or measurements.

Answer: Quantitative

Worked Example 3

Problem: Classify the data values [3, 5, 8, 8, 11] as quantitative or qualitative.

  1. They are numerical values.
  2. Numerical counts or measurements are quantitative.

Very beginner explanation: Quantitative data use numbers to represent counts or measurements.

Answer: Quantitative

Worked Example 4

Problem: Classify the data values [10, 12, 14, 16] as quantitative or qualitative.

  1. They are numerical values.
  2. Numerical counts or measurements are quantitative.

Very beginner explanation: Quantitative data use numbers to represent counts or measurements.

Answer: Quantitative

Worked Example 5

Problem: Classify the data values [2, 4, 6, 8, 10] as quantitative or qualitative.

  1. They are numerical values.
  2. Numerical counts or measurements are quantitative.

Very beginner explanation: Quantitative data use numbers to represent counts or measurements.

Answer: Quantitative

Worked Example 6

Problem: Classify the data values [1, 5, 5, 6, 13] as quantitative or qualitative.

  1. They are numerical values.
  2. Numerical counts or measurements are quantitative.

Very beginner explanation: Quantitative data use numbers to represent counts or measurements.

Answer: Quantitative

Worked Example 7

Problem: Classify the data values [20, 25, 25, 30] as quantitative or qualitative.

  1. They are numerical values.
  2. Numerical counts or measurements are quantitative.

Very beginner explanation: Quantitative data use numbers to represent counts or measurements.

Answer: Quantitative

Worked Example 8

Problem: Classify the data values [7, 8, 9, 10, 11] as quantitative or qualitative.

  1. They are numerical values.
  2. Numerical counts or measurements are quantitative.

Very beginner explanation: Quantitative data use numbers to represent counts or measurements.

Answer: Quantitative

Worked Example 9

Problem: Classify the data values [3, 3, 4, 5, 9] as quantitative or qualitative.

  1. They are numerical values.
  2. Numerical counts or measurements are quantitative.

Very beginner explanation: Quantitative data use numbers to represent counts or measurements.

Answer: Quantitative

Worked Example 10

Problem: Classify the data values [12, 15, 18, 21] as quantitative or qualitative.

  1. They are numerical values.
  2. Numerical counts or measurements are quantitative.

Very beginner explanation: Quantitative data use numbers to represent counts or measurements.

Answer: Quantitative

Practice Exercise

Create one new Grade 6 problem about Continuous numerical data. 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.

40.5 Choosing interval widths

Choosing interval widths is a Grade 6 mathematics idea in Histograms. 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 interval widths to analyze the values 27 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: Choosing interval widths is a Grade 6 mathematics idea in Histograms. 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 interval widths to analyze the values 15 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 interval widths is a Grade 6 mathematics idea in Histograms. 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 interval widths to analyze the values 23 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: Choosing interval widths is a Grade 6 mathematics idea in Histograms. 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 interval widths to analyze the values 18 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 interval widths is a Grade 6 mathematics idea in Histograms. 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 interval widths to analyze the values 27 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 interval widths is a Grade 6 mathematics idea in Histograms. 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 interval widths to analyze the values 5 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: Choosing interval widths is a Grade 6 mathematics idea in Histograms. 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 interval widths to analyze the values 7 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: Choosing interval widths is a Grade 6 mathematics idea in Histograms. 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 interval widths to analyze the values 29 and 16. 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 interval widths is a Grade 6 mathematics idea in Histograms. 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 interval widths to analyze the values 9 and 19. 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 interval widths is a Grade 6 mathematics idea in Histograms. 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 interval widths to analyze the values 25 and 11. 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 interval widths is a Grade 6 mathematics idea in Histograms. 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 interval widths. 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.

40.6 Reading a histogram

A histogram groups numerical data into intervals and shows the frequency in each interval. 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: A histogram interval 0–9 has frequency 3. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 3 data value(s) fall from 0 through 9.

Worked Example 2

Problem: A histogram interval 0–9 has frequency 4. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 4 data value(s) fall from 0 through 9.

Worked Example 3

Problem: A histogram interval 0–9 has frequency 4. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 4 data value(s) fall from 0 through 9.

Worked Example 4

Problem: A histogram interval 0–9 has frequency 0. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 0 data value(s) fall from 0 through 9.

Worked Example 5

Problem: A histogram interval 0–9 has frequency 4. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 4 data value(s) fall from 0 through 9.

Worked Example 6

Problem: A histogram interval 0–9 has frequency 4. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 4 data value(s) fall from 0 through 9.

Worked Example 7

Problem: A histogram interval 0–9 has frequency 0. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 0 data value(s) fall from 0 through 9.

Worked Example 8

Problem: A histogram interval 0–9 has frequency 3. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 3 data value(s) fall from 0 through 9.

Worked Example 9

Problem: A histogram interval 0–9 has frequency 5. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 5 data value(s) fall from 0 through 9.

Worked Example 10

Problem: A histogram interval 0–9 has frequency 0. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 0 data value(s) fall from 0 through 9.

Practice Exercise

Create one new Grade 6 problem about Reading a histogram. 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.

40.7 Creating a histogram

A histogram groups numerical data into intervals and shows the frequency in each interval. 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: A histogram interval 0–9 has frequency 3. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 3 data value(s) fall from 0 through 9.

Worked Example 2

Problem: A histogram interval 0–9 has frequency 4. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 4 data value(s) fall from 0 through 9.

Worked Example 3

Problem: A histogram interval 0–9 has frequency 4. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 4 data value(s) fall from 0 through 9.

Worked Example 4

Problem: A histogram interval 0–9 has frequency 0. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 0 data value(s) fall from 0 through 9.

Worked Example 5

Problem: A histogram interval 0–9 has frequency 4. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 4 data value(s) fall from 0 through 9.

Worked Example 6

Problem: A histogram interval 0–9 has frequency 4. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 4 data value(s) fall from 0 through 9.

Worked Example 7

Problem: A histogram interval 0–9 has frequency 0. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 0 data value(s) fall from 0 through 9.

Worked Example 8

Problem: A histogram interval 0–9 has frequency 3. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 3 data value(s) fall from 0 through 9.

Worked Example 9

Problem: A histogram interval 0–9 has frequency 5. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 5 data value(s) fall from 0 through 9.

Worked Example 10

Problem: A histogram interval 0–9 has frequency 0. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 0 data value(s) fall from 0 through 9.

Practice Exercise

Create one new Grade 6 problem about Creating a histogram. 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.

40.8 Comparing histogram bars

A histogram groups numerical data into intervals and shows the frequency in each interval. 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: A histogram interval 0–9 has frequency 3. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 3 data value(s) fall from 0 through 9.

Worked Example 2

Problem: A histogram interval 0–9 has frequency 4. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 4 data value(s) fall from 0 through 9.

Worked Example 3

Problem: A histogram interval 0–9 has frequency 4. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 4 data value(s) fall from 0 through 9.

Worked Example 4

Problem: A histogram interval 0–9 has frequency 0. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 0 data value(s) fall from 0 through 9.

Worked Example 5

Problem: A histogram interval 0–9 has frequency 4. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 4 data value(s) fall from 0 through 9.

Worked Example 6

Problem: A histogram interval 0–9 has frequency 4. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 4 data value(s) fall from 0 through 9.

Worked Example 7

Problem: A histogram interval 0–9 has frequency 0. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 0 data value(s) fall from 0 through 9.

Worked Example 8

Problem: A histogram interval 0–9 has frequency 3. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 3 data value(s) fall from 0 through 9.

Worked Example 9

Problem: A histogram interval 0–9 has frequency 5. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 5 data value(s) fall from 0 through 9.

Worked Example 10

Problem: A histogram interval 0–9 has frequency 0. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 0 data value(s) fall from 0 through 9.

Practice Exercise

Create one new Grade 6 problem about Comparing histogram bars. 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.

40.9 Identifying clusters

Identifying clusters is a Grade 6 mathematics idea in Histograms. 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 Identifying clusters to analyze the values 18 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: Identifying clusters is a Grade 6 mathematics idea in Histograms. 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 Identifying clusters 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: Identifying clusters is a Grade 6 mathematics idea in Histograms. 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 Identifying clusters to analyze the values 14 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: Identifying clusters is a Grade 6 mathematics idea in Histograms. 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 Identifying clusters to analyze the values 18 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: Identifying clusters is a Grade 6 mathematics idea in Histograms. 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 Identifying clusters to analyze the values 6 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: Identifying clusters is a Grade 6 mathematics idea in Histograms. 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 Identifying clusters to analyze the values 29 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: Identifying clusters is a Grade 6 mathematics idea in Histograms. 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 Identifying clusters to analyze the values 11 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: Identifying clusters is a Grade 6 mathematics idea in Histograms. 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 Identifying clusters to analyze the values 27 and 16. 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: Identifying clusters is a Grade 6 mathematics idea in Histograms. 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 Identifying clusters to analyze the values 14 and 3. 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: Identifying clusters is a Grade 6 mathematics idea in Histograms. 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 Identifying clusters to analyze the values 19 and 19. 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: Identifying clusters is a Grade 6 mathematics idea in Histograms. 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 Identifying clusters. 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.

40.10 Identifying gaps

Identifying gaps is a Grade 6 mathematics idea in Histograms. 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 Identifying gaps to analyze the values 13 and 16. 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: Identifying gaps is a Grade 6 mathematics idea in Histograms. 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 Identifying gaps to analyze the values 8 and 19. 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: Identifying gaps is a Grade 6 mathematics idea in Histograms. 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 Identifying gaps to analyze the values 19 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: Identifying gaps is a Grade 6 mathematics idea in Histograms. 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 Identifying gaps to analyze the values 24 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: Identifying gaps is a Grade 6 mathematics idea in Histograms. 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 Identifying gaps 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: Identifying gaps is a Grade 6 mathematics idea in Histograms. 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 Identifying gaps to analyze the values 29 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: Identifying gaps is a Grade 6 mathematics idea in Histograms. 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 Identifying gaps to analyze the values 20 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: Identifying gaps is a Grade 6 mathematics idea in Histograms. 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 Identifying gaps to analyze the values 25 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: Identifying gaps is a Grade 6 mathematics idea in Histograms. 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 Identifying gaps to analyze the values 29 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: Identifying gaps is a Grade 6 mathematics idea in Histograms. 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 Identifying gaps 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: Identifying gaps is a Grade 6 mathematics idea in Histograms. 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 Identifying gaps. 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.

40.11 Drawing conclusions

Drawing conclusions is a Grade 6 mathematics idea in Histograms. 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 Drawing conclusions to analyze the values 23 and 11. 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: Drawing conclusions is a Grade 6 mathematics idea in Histograms. 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 Drawing conclusions to analyze the values 28 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: Drawing conclusions is a Grade 6 mathematics idea in Histograms. 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 Drawing conclusions to analyze the values 4 and 16. 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: Drawing conclusions is a Grade 6 mathematics idea in Histograms. 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 Drawing conclusions to analyze the values 15 and 19. 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: Drawing conclusions is a Grade 6 mathematics idea in Histograms. 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 Drawing conclusions to analyze the values 3 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: Drawing conclusions is a Grade 6 mathematics idea in Histograms. 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 Drawing conclusions to analyze the values 26 and 3. 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: Drawing conclusions is a Grade 6 mathematics idea in Histograms. 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 Drawing conclusions to analyze the values 17 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: Drawing conclusions is a Grade 6 mathematics idea in Histograms. 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 Drawing conclusions to analyze the values 3 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: Drawing conclusions is a Grade 6 mathematics idea in Histograms. 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 Drawing conclusions to analyze the values 15 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: Drawing conclusions is a Grade 6 mathematics idea in Histograms. 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 Drawing conclusions to analyze the values 5 and 11. 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: Drawing conclusions is a Grade 6 mathematics idea in Histograms. 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 Drawing conclusions. 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.

40.12 Histogram mistakes

A histogram groups numerical data into intervals and shows the frequency in each interval. 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: A histogram interval 0–9 has frequency 3. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 3 data value(s) fall from 0 through 9.

Worked Example 2

Problem: A histogram interval 0–9 has frequency 4. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 4 data value(s) fall from 0 through 9.

Worked Example 3

Problem: A histogram interval 0–9 has frequency 4. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 4 data value(s) fall from 0 through 9.

Worked Example 4

Problem: A histogram interval 0–9 has frequency 0. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 0 data value(s) fall from 0 through 9.

Worked Example 5

Problem: A histogram interval 0–9 has frequency 4. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 4 data value(s) fall from 0 through 9.

Worked Example 6

Problem: A histogram interval 0–9 has frequency 4. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 4 data value(s) fall from 0 through 9.

Worked Example 7

Problem: A histogram interval 0–9 has frequency 0. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 0 data value(s) fall from 0 through 9.

Worked Example 8

Problem: A histogram interval 0–9 has frequency 3. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 3 data value(s) fall from 0 through 9.

Worked Example 9

Problem: A histogram interval 0–9 has frequency 5. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 5 data value(s) fall from 0 through 9.

Worked Example 10

Problem: A histogram interval 0–9 has frequency 0. What does that frequency mean?

  1. Identify the interval.
  2. Count values in the interval.

Very beginner explanation: Histogram frequency tells how many data values fall inside an interval.

Answer: 0 data value(s) fall from 0 through 9.

Practice Exercise

Create one new Grade 6 problem about Histogram mistakes. 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 Meaning of histogram?

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

Q2. What is important to understand about Intervals?

Answer: Intervals is a Grade 6 mathematics idea in Histograms. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q3. What is important to understand about Frequency?

Answer: Frequency is a Grade 6 mathematics idea in Histograms. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q4. What is important to understand about Continuous numerical data?

Answer: Continuous numerical data is a Grade 6 mathematics idea in Histograms. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q5. What is important to understand about Choosing interval widths?

Answer: Choosing interval widths is a Grade 6 mathematics idea in Histograms. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q6. What is important to understand about Reading a histogram?

Answer: A histogram groups numerical data into intervals and shows the frequency in each interval.

Q7. What is important to understand about Creating a histogram?

Answer: A histogram groups numerical data into intervals and shows the frequency in each interval.

Q8. What is important to understand about Comparing histogram bars?

Answer: A histogram groups numerical data into intervals and shows the frequency in each interval.

Q9. What is important to understand about Identifying clusters?

Answer: Identifying clusters is a Grade 6 mathematics idea in Histograms. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q10. What is important to understand about Identifying gaps?

Answer: Identifying gaps is a Grade 6 mathematics idea in Histograms. 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 Drawing conclusions?

Answer: Drawing conclusions is a Grade 6 mathematics idea in Histograms. 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 Histogram mistakes?

Answer: A histogram groups numerical data into intervals and shows the frequency in each interval.

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.