Chapter 41: Mean, Median, Mode, Range, and Data Comparisons
Learn Grade 7 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Mean, Median, Mode, Range, and Data Comparisons with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.
Key Technical Terms
- Estimate (a close approximation used to check whether an answer is reasonable)
- Solution (a value or result that satisfies the problem)
- Representation (a way to show mathematics using symbols, diagrams, tables, graphs, or words)
- Reasonableness (whether an answer makes sense in the context of the problem)
How to Learn This Chapter
Read the explanation first, follow the examples one step at a time, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.
41.1 Mean
The mean is the sum of all values divided by the number of values. This topic focuses on Mean .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Find mean of [4, 6, 8].
- Sum=18.
- Divide by 3.
Very beginner explanation: The mean is the sum of all values divided by the number of values. This topic focuses on Mean .
Answer: 6
Worked Example 2
Problem: Find mean of [5, 9, 10, 12].
- Sum=36.
- Divide by 4.
Very beginner explanation: The mean is the sum of all values divided by the number of values. This topic focuses on Mean .
Answer: 9
Worked Example 3
Problem: Find mean of [3, 7, 7, 11].
- Sum=28.
- Divide by 4.
Very beginner explanation: The mean is the sum of all values divided by the number of values. This topic focuses on Mean .
Answer: 7
Worked Example 4
Problem: Find mean of [20, 25, 30].
- Sum=75.
- Divide by 3.
Very beginner explanation: The mean is the sum of all values divided by the number of values. This topic focuses on Mean .
Answer: 25
Worked Example 5
Problem: Find mean of [6, 8, 9, 12, 15].
- Sum=50.
- Divide by 5.
Very beginner explanation: The mean is the sum of all values divided by the number of values. This topic focuses on Mean .
Answer: 10
Worked Example 6
Problem: Find the mean of [4, 6, 8].
- Add the values: 18.
- Divide by 3.
Very beginner explanation: The mean is the total shared equally among all values.
Answer: 6
Worked Example 7
Problem: Find the mean of [5, 9, 10, 12].
- Add the values: 36.
- Divide by 4.
Very beginner explanation: The mean is the total shared equally among all values.
Answer: 9
Worked Example 8
Problem: Find the mean of [3, 7, 7, 11].
- Add the values: 28.
- Divide by 4.
Very beginner explanation: The mean is the total shared equally among all values.
Answer: 7
Worked Example 9
Problem: Find the mean of [20, 25, 30].
- Add the values: 75.
- Divide by 3.
Very beginner explanation: The mean is the total shared equally among all values.
Answer: 25
Worked Example 10
Problem: Find the mean of [6, 8, 9, 12, 15].
- Add the values: 50.
- Divide by 5.
Very beginner explanation: The mean is the total shared equally among all values.
Answer: 10
Practice Exercise
Create one new question about Mean. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
41.2 Median
The median is the middle value after data are put in order. This topic focuses on Median .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Find median of [4, 6, 8].
- Order the values.
- Choose the middle value or average the two middle values.
Very beginner explanation: The median is the middle value after data are put in order. This topic focuses on Median .
Answer: 6
Worked Example 2
Problem: Find median of [5, 9, 10, 12].
- Order the values.
- Choose the middle value or average the two middle values.
Very beginner explanation: The median is the middle value after data are put in order. This topic focuses on Median .
Answer: 9.5
Worked Example 3
Problem: Find median of [3, 7, 7, 11].
- Order the values.
- Choose the middle value or average the two middle values.
Very beginner explanation: The median is the middle value after data are put in order. This topic focuses on Median .
Answer: 7
Worked Example 4
Problem: Find median of [20, 25, 30].
- Order the values.
- Choose the middle value or average the two middle values.
Very beginner explanation: The median is the middle value after data are put in order. This topic focuses on Median .
Answer: 25
Worked Example 5
Problem: Find median of [6, 8, 9, 12, 15].
- Order the values.
- Choose the middle value or average the two middle values.
Very beginner explanation: The median is the middle value after data are put in order. This topic focuses on Median .
Answer: 9
Worked Example 6
Problem: Find the median of [4, 6, 8].
- Order the values.
- Choose the middle value, or average the two middle values.
Very beginner explanation: Median depends on position after sorting.
Answer: 6
Worked Example 7
Problem: Find the median of [5, 9, 10, 12].
- Order the values.
- Choose the middle value, or average the two middle values.
Very beginner explanation: Median depends on position after sorting.
Answer: 9.5
Worked Example 8
Problem: Find the median of [3, 7, 7, 11].
- Order the values.
- Choose the middle value, or average the two middle values.
Very beginner explanation: Median depends on position after sorting.
Answer: 7
Worked Example 9
Problem: Find the median of [20, 25, 30].
- Order the values.
- Choose the middle value, or average the two middle values.
Very beginner explanation: Median depends on position after sorting.
Answer: 25
Worked Example 10
Problem: Find the median of [6, 8, 9, 12, 15].
- Order the values.
- Choose the middle value, or average the two middle values.
Very beginner explanation: Median depends on position after sorting.
Answer: 9
Practice Exercise
Create one new question about Median. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
41.3 Mode
The mode is the value that occurs most often. This topic focuses on Mode .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Find mode of [4, 6, 8].
- Count each value's frequency.
Very beginner explanation: The mode is the value that occurs most often. This topic focuses on Mode .
Answer: No mode
Worked Example 2
Problem: Find mode of [5, 9, 10, 12].
- Count each value's frequency.
Very beginner explanation: The mode is the value that occurs most often. This topic focuses on Mode .
Answer: No mode
Worked Example 3
Problem: Find mode of [3, 7, 7, 11].
- Count each value's frequency.
Very beginner explanation: The mode is the value that occurs most often. This topic focuses on Mode .
Answer: 7
Worked Example 4
Problem: Find mode of [20, 25, 30].
- Count each value's frequency.
Very beginner explanation: The mode is the value that occurs most often. This topic focuses on Mode .
Answer: No mode
Worked Example 5
Problem: Find mode of [6, 8, 9, 12, 15].
- Count each value's frequency.
Very beginner explanation: The mode is the value that occurs most often. This topic focuses on Mode .
Answer: No mode
Worked Example 6
Problem: Find the mode of [4, 6, 8].
- Count how often each value occurs.
Very beginner explanation: Mode is the value that occurs most often.
Answer: No mode
Worked Example 7
Problem: Find the mode of [5, 9, 10, 12].
- Count how often each value occurs.
Very beginner explanation: Mode is the value that occurs most often.
Answer: No mode
Worked Example 8
Problem: Find the mode of [3, 7, 7, 11].
- Count how often each value occurs.
Very beginner explanation: Mode is the value that occurs most often.
Answer: 7
Worked Example 9
Problem: Find the mode of [20, 25, 30].
- Count how often each value occurs.
Very beginner explanation: Mode is the value that occurs most often.
Answer: No mode
Worked Example 10
Problem: Find the mode of [6, 8, 9, 12, 15].
- Count how often each value occurs.
Very beginner explanation: Mode is the value that occurs most often.
Answer: No mode
Practice Exercise
Create one new question about Mode. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
41.4 Range
The range is the greatest value minus the least value. This topic focuses on Range .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Find range of [4, 6, 8].
- Greatest minus least.
Very beginner explanation: The range is the greatest value minus the least value. This topic focuses on Range .
Answer: 4
Worked Example 2
Problem: Find range of [5, 9, 10, 12].
- Greatest minus least.
Very beginner explanation: The range is the greatest value minus the least value. This topic focuses on Range .
Answer: 7
Worked Example 3
Problem: Find range of [3, 7, 7, 11].
- Greatest minus least.
Very beginner explanation: The range is the greatest value minus the least value. This topic focuses on Range .
Answer: 8
Worked Example 4
Problem: Find range of [20, 25, 30].
- Greatest minus least.
Very beginner explanation: The range is the greatest value minus the least value. This topic focuses on Range .
Answer: 10
Worked Example 5
Problem: Find range of [6, 8, 9, 12, 15].
- Greatest minus least.
Very beginner explanation: The range is the greatest value minus the least value. This topic focuses on Range .
Answer: 9
Worked Example 6
Problem: Find the range of [4, 6, 8].
- Find the greatest value.
- Find the least value.
- Subtract least from greatest.
Very beginner explanation: Range is a simple measure of how spread out the values are.
Answer: 4
Worked Example 7
Problem: Find the range of [5, 9, 10, 12].
- Find the greatest value.
- Find the least value.
- Subtract least from greatest.
Very beginner explanation: Range is a simple measure of how spread out the values are.
Answer: 7
Worked Example 8
Problem: Find the range of [3, 7, 7, 11].
- Find the greatest value.
- Find the least value.
- Subtract least from greatest.
Very beginner explanation: Range is a simple measure of how spread out the values are.
Answer: 8
Worked Example 9
Problem: Find the range of [20, 25, 30].
- Find the greatest value.
- Find the least value.
- Subtract least from greatest.
Very beginner explanation: Range is a simple measure of how spread out the values are.
Answer: 10
Worked Example 10
Problem: Find the range of [6, 8, 9, 12, 15].
- Find the greatest value.
- Find the least value.
- Subtract least from greatest.
Very beginner explanation: Range is a simple measure of how spread out the values are.
Answer: 9
Practice Exercise
Create one new question about Range. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
41.5 Calculating mean
The mean is the sum of all values divided by the number of values. This topic focuses on Calculating mean .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Find mean of [4, 6, 8].
- Sum=18.
- Divide by 3.
Very beginner explanation: The mean is the sum of all values divided by the number of values. This topic focuses on Calculating mean .
Answer: 6
Worked Example 2
Problem: Find mean of [5, 9, 10, 12].
- Sum=36.
- Divide by 4.
Very beginner explanation: The mean is the sum of all values divided by the number of values. This topic focuses on Calculating mean .
Answer: 9
Worked Example 3
Problem: Find mean of [3, 7, 7, 11].
- Sum=28.
- Divide by 4.
Very beginner explanation: The mean is the sum of all values divided by the number of values. This topic focuses on Calculating mean .
Answer: 7
Worked Example 4
Problem: Find mean of [20, 25, 30].
- Sum=75.
- Divide by 3.
Very beginner explanation: The mean is the sum of all values divided by the number of values. This topic focuses on Calculating mean .
Answer: 25
Worked Example 5
Problem: Find mean of [6, 8, 9, 12, 15].
- Sum=50.
- Divide by 5.
Very beginner explanation: The mean is the sum of all values divided by the number of values. This topic focuses on Calculating mean .
Answer: 10
Worked Example 6
Problem: Find the mean of [4, 6, 8].
- Add the values: 18.
- Divide by 3.
Very beginner explanation: The mean is the total shared equally among all values.
Answer: 6
Worked Example 7
Problem: Find the mean of [5, 9, 10, 12].
- Add the values: 36.
- Divide by 4.
Very beginner explanation: The mean is the total shared equally among all values.
Answer: 9
Worked Example 8
Problem: Find the mean of [3, 7, 7, 11].
- Add the values: 28.
- Divide by 4.
Very beginner explanation: The mean is the total shared equally among all values.
Answer: 7
Worked Example 9
Problem: Find the mean of [20, 25, 30].
- Add the values: 75.
- Divide by 3.
Very beginner explanation: The mean is the total shared equally among all values.
Answer: 25
Worked Example 10
Problem: Find the mean of [6, 8, 9, 12, 15].
- Add the values: 50.
- Divide by 5.
Very beginner explanation: The mean is the total shared equally among all values.
Answer: 10
Practice Exercise
Create one new question about Calculating mean. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
41.6 Finding median
The median is the middle value after data are put in order. This topic focuses on Finding median .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Find median of [4, 6, 8].
- Order the values.
- Choose the middle value or average the two middle values.
Very beginner explanation: The median is the middle value after data are put in order. This topic focuses on Finding median .
Answer: 6
Worked Example 2
Problem: Find median of [5, 9, 10, 12].
- Order the values.
- Choose the middle value or average the two middle values.
Very beginner explanation: The median is the middle value after data are put in order. This topic focuses on Finding median .
Answer: 9.5
Worked Example 3
Problem: Find median of [3, 7, 7, 11].
- Order the values.
- Choose the middle value or average the two middle values.
Very beginner explanation: The median is the middle value after data are put in order. This topic focuses on Finding median .
Answer: 7
Worked Example 4
Problem: Find median of [20, 25, 30].
- Order the values.
- Choose the middle value or average the two middle values.
Very beginner explanation: The median is the middle value after data are put in order. This topic focuses on Finding median .
Answer: 25
Worked Example 5
Problem: Find median of [6, 8, 9, 12, 15].
- Order the values.
- Choose the middle value or average the two middle values.
Very beginner explanation: The median is the middle value after data are put in order. This topic focuses on Finding median .
Answer: 9
Worked Example 6
Problem: Find the median of [4, 6, 8].
- Order the values.
- Choose the middle value, or average the two middle values.
Very beginner explanation: Median depends on position after sorting.
Answer: 6
Worked Example 7
Problem: Find the median of [5, 9, 10, 12].
- Order the values.
- Choose the middle value, or average the two middle values.
Very beginner explanation: Median depends on position after sorting.
Answer: 9.5
Worked Example 8
Problem: Find the median of [3, 7, 7, 11].
- Order the values.
- Choose the middle value, or average the two middle values.
Very beginner explanation: Median depends on position after sorting.
Answer: 7
Worked Example 9
Problem: Find the median of [20, 25, 30].
- Order the values.
- Choose the middle value, or average the two middle values.
Very beginner explanation: Median depends on position after sorting.
Answer: 25
Worked Example 10
Problem: Find the median of [6, 8, 9, 12, 15].
- Order the values.
- Choose the middle value, or average the two middle values.
Very beginner explanation: Median depends on position after sorting.
Answer: 9
Practice Exercise
Create one new question about Finding median. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
41.7 Finding mode
The mode is the value that occurs most often. This topic focuses on Finding mode .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Find mode of [4, 6, 8].
- Count each value's frequency.
Very beginner explanation: The mode is the value that occurs most often. This topic focuses on Finding mode .
Answer: No mode
Worked Example 2
Problem: Find mode of [5, 9, 10, 12].
- Count each value's frequency.
Very beginner explanation: The mode is the value that occurs most often. This topic focuses on Finding mode .
Answer: No mode
Worked Example 3
Problem: Find mode of [3, 7, 7, 11].
- Count each value's frequency.
Very beginner explanation: The mode is the value that occurs most often. This topic focuses on Finding mode .
Answer: 7
Worked Example 4
Problem: Find mode of [20, 25, 30].
- Count each value's frequency.
Very beginner explanation: The mode is the value that occurs most often. This topic focuses on Finding mode .
Answer: No mode
Worked Example 5
Problem: Find mode of [6, 8, 9, 12, 15].
- Count each value's frequency.
Very beginner explanation: The mode is the value that occurs most often. This topic focuses on Finding mode .
Answer: No mode
Worked Example 6
Problem: Find the mode of [4, 6, 8].
- Count how often each value occurs.
Very beginner explanation: Mode is the value that occurs most often.
Answer: No mode
Worked Example 7
Problem: Find the mode of [5, 9, 10, 12].
- Count how often each value occurs.
Very beginner explanation: Mode is the value that occurs most often.
Answer: No mode
Worked Example 8
Problem: Find the mode of [3, 7, 7, 11].
- Count how often each value occurs.
Very beginner explanation: Mode is the value that occurs most often.
Answer: 7
Worked Example 9
Problem: Find the mode of [20, 25, 30].
- Count how often each value occurs.
Very beginner explanation: Mode is the value that occurs most often.
Answer: No mode
Worked Example 10
Problem: Find the mode of [6, 8, 9, 12, 15].
- Count how often each value occurs.
Very beginner explanation: Mode is the value that occurs most often.
Answer: No mode
Practice Exercise
Create one new question about Finding mode. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
41.8 Finding range
The range is the greatest value minus the least value. This topic focuses on Finding range .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Find range of [4, 6, 8].
- Greatest minus least.
Very beginner explanation: The range is the greatest value minus the least value. This topic focuses on Finding range .
Answer: 4
Worked Example 2
Problem: Find range of [5, 9, 10, 12].
- Greatest minus least.
Very beginner explanation: The range is the greatest value minus the least value. This topic focuses on Finding range .
Answer: 7
Worked Example 3
Problem: Find range of [3, 7, 7, 11].
- Greatest minus least.
Very beginner explanation: The range is the greatest value minus the least value. This topic focuses on Finding range .
Answer: 8
Worked Example 4
Problem: Find range of [20, 25, 30].
- Greatest minus least.
Very beginner explanation: The range is the greatest value minus the least value. This topic focuses on Finding range .
Answer: 10
Worked Example 5
Problem: Find range of [6, 8, 9, 12, 15].
- Greatest minus least.
Very beginner explanation: The range is the greatest value minus the least value. This topic focuses on Finding range .
Answer: 9
Worked Example 6
Problem: Find the range of [4, 6, 8].
- Find the greatest value.
- Find the least value.
- Subtract least from greatest.
Very beginner explanation: Range is a simple measure of how spread out the values are.
Answer: 4
Worked Example 7
Problem: Find the range of [5, 9, 10, 12].
- Find the greatest value.
- Find the least value.
- Subtract least from greatest.
Very beginner explanation: Range is a simple measure of how spread out the values are.
Answer: 7
Worked Example 8
Problem: Find the range of [3, 7, 7, 11].
- Find the greatest value.
- Find the least value.
- Subtract least from greatest.
Very beginner explanation: Range is a simple measure of how spread out the values are.
Answer: 8
Worked Example 9
Problem: Find the range of [20, 25, 30].
- Find the greatest value.
- Find the least value.
- Subtract least from greatest.
Very beginner explanation: Range is a simple measure of how spread out the values are.
Answer: 10
Worked Example 10
Problem: Find the range of [6, 8, 9, 12, 15].
- Find the greatest value.
- Find the least value.
- Subtract least from greatest.
Very beginner explanation: Range is a simple measure of how spread out the values are.
Answer: 9
Practice Exercise
Create one new question about Finding range. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
41.9 Outliers
Outliers is an important Grade 7 idea in Mean, Median, Mode, Range, and Data Comparisons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Find mean of [4, 6, 8].
- Sum=18.
- Divide by 3.
Very beginner explanation: Outliers is an important Grade 7 idea in Mean, Median, Mode, Range, and Data Comparisons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 6
Worked Example 2
Problem: Find mean of [5, 9, 10, 12].
- Sum=36.
- Divide by 4.
Very beginner explanation: Outliers is an important Grade 7 idea in Mean, Median, Mode, Range, and Data Comparisons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 9
Worked Example 3
Problem: Find mean of [3, 7, 7, 11].
- Sum=28.
- Divide by 4.
Very beginner explanation: Outliers is an important Grade 7 idea in Mean, Median, Mode, Range, and Data Comparisons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 7
Worked Example 4
Problem: Find mean of [20, 25, 30].
- Sum=75.
- Divide by 3.
Very beginner explanation: Outliers is an important Grade 7 idea in Mean, Median, Mode, Range, and Data Comparisons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 25
Worked Example 5
Problem: Find mean of [6, 8, 9, 12, 15].
- Sum=50.
- Divide by 5.
Very beginner explanation: Outliers is an important Grade 7 idea in Mean, Median, Mode, Range, and Data Comparisons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 10
Worked Example 6
Problem: Classify the data [4, 6, 8].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 7
Problem: Classify the data [5, 9, 10, 12].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 8
Problem: Classify the data [3, 7, 7, 11].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 9
Problem: Classify the data [20, 25, 30].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 10
Problem: Classify the data [6, 8, 9, 12, 15].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Practice Exercise
Create one new question about Outliers. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
41.10 Effect of outliers on mean
The mean is the sum of all values divided by the number of values. This topic focuses on Effect of outliers on mean .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Find mean of [4, 6, 8].
- Sum=18.
- Divide by 3.
Very beginner explanation: The mean is the sum of all values divided by the number of values. This topic focuses on Effect of outliers on mean .
Answer: 6
Worked Example 2
Problem: Find mean of [5, 9, 10, 12].
- Sum=36.
- Divide by 4.
Very beginner explanation: The mean is the sum of all values divided by the number of values. This topic focuses on Effect of outliers on mean .
Answer: 9
Worked Example 3
Problem: Find mean of [3, 7, 7, 11].
- Sum=28.
- Divide by 4.
Very beginner explanation: The mean is the sum of all values divided by the number of values. This topic focuses on Effect of outliers on mean .
Answer: 7
Worked Example 4
Problem: Find mean of [20, 25, 30].
- Sum=75.
- Divide by 3.
Very beginner explanation: The mean is the sum of all values divided by the number of values. This topic focuses on Effect of outliers on mean .
Answer: 25
Worked Example 5
Problem: Find mean of [6, 8, 9, 12, 15].
- Sum=50.
- Divide by 5.
Very beginner explanation: The mean is the sum of all values divided by the number of values. This topic focuses on Effect of outliers on mean .
Answer: 10
Worked Example 6
Problem: Find the mean of [4, 6, 8].
- Add the values: 18.
- Divide by 3.
Very beginner explanation: The mean is the total shared equally among all values.
Answer: 6
Worked Example 7
Problem: Find the mean of [5, 9, 10, 12].
- Add the values: 36.
- Divide by 4.
Very beginner explanation: The mean is the total shared equally among all values.
Answer: 9
Worked Example 8
Problem: Find the mean of [3, 7, 7, 11].
- Add the values: 28.
- Divide by 4.
Very beginner explanation: The mean is the total shared equally among all values.
Answer: 7
Worked Example 9
Problem: Find the mean of [20, 25, 30].
- Add the values: 75.
- Divide by 3.
Very beginner explanation: The mean is the total shared equally among all values.
Answer: 25
Worked Example 10
Problem: Find the mean of [6, 8, 9, 12, 15].
- Add the values: 50.
- Divide by 5.
Very beginner explanation: The mean is the total shared equally among all values.
Answer: 10
Practice Exercise
Create one new question about Effect of outliers on mean. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
41.11 Comparing two data sets
Data are observations, measurements, or categories collected to answer questions. This topic focuses on Comparing two data sets .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Favourite school subject
- Classify it as categorical/qualitative data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Comparing two data sets .
Answer: Use a frequency table
Worked Example 2
Problem: Student heights
- Classify it as quantitative continuous data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Comparing two data sets .
Answer: Measure in centimetres
Worked Example 3
Problem: Number of siblings
- Classify it as quantitative discrete data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Comparing two data sets .
Answer: Count whole numbers
Worked Example 4
Problem: Survey every 10th student
- Classify it as systematic sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Comparing two data sets .
Answer: Check that the list order does not create bias
Worked Example 5
Problem: Survey only basketball team members about school sports
- Classify it as biased sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Comparing two data sets .
Answer: Broaden the sample
Worked Example 6
Problem: Classify the data [4, 6, 8].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 7
Problem: Classify the data [5, 9, 10, 12].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 8
Problem: Classify the data [3, 7, 7, 11].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 9
Problem: Classify the data [20, 25, 30].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 10
Problem: Classify the data [6, 8, 9, 12, 15].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Practice Exercise
Create one new question about Comparing two data sets. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
41.12 Choosing a useful measure
Choosing a useful measure is an important Grade 7 idea in Mean, Median, Mode, Range, and Data Comparisons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Choosing a useful measure: Identify a correct example.
- State the definition and show why the example fits.
- Show all important reasoning.
Very beginner explanation: Choosing a useful measure is an important Grade 7 idea in Mean, Median, Mode, Range, and Data Comparisons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 2
Problem: Choosing a useful measure: Identify a non-example.
- Explain which requirement is missing.
- Show all important reasoning.
Very beginner explanation: Choosing a useful measure is an important Grade 7 idea in Mean, Median, Mode, Range, and Data Comparisons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 3
Problem: Choosing a useful measure: Compare two cases.
- State one similarity and one difference.
- Show all important reasoning.
Very beginner explanation: Choosing a useful measure is an important Grade 7 idea in Mean, Median, Mode, Range, and Data Comparisons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 4
Problem: Choosing a useful measure: Apply the idea in a real situation.
- Translate the situation into mathematical language.
- Show all important reasoning.
Very beginner explanation: Choosing a useful measure is an important Grade 7 idea in Mean, Median, Mode, Range, and Data Comparisons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 5
Problem: Choosing a useful measure: Create and check your own example.
- Use the definition, then verify each condition.
- Show all important reasoning.
Very beginner explanation: Choosing a useful measure is an important Grade 7 idea in Mean, Median, Mode, Range, and Data Comparisons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 6
Problem: Explain Choosing a useful measure in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Choosing a useful measure becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Choosing a useful measure and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Choosing a useful measure becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Choosing a useful measure using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Choosing a useful measure becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Choosing a useful measure problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Choosing a useful measure becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Choosing a useful measure could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Choosing a useful measure becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Choosing a useful measure. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
41.13 Interpreting averages
Interpreting averages is an important Grade 7 idea in Mean, Median, Mode, Range, and Data Comparisons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Find mean of [4, 6, 8].
- Sum=18.
- Divide by 3.
Very beginner explanation: Interpreting averages is an important Grade 7 idea in Mean, Median, Mode, Range, and Data Comparisons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 6
Worked Example 2
Problem: Find mean of [5, 9, 10, 12].
- Sum=36.
- Divide by 4.
Very beginner explanation: Interpreting averages is an important Grade 7 idea in Mean, Median, Mode, Range, and Data Comparisons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 9
Worked Example 3
Problem: Find mean of [3, 7, 7, 11].
- Sum=28.
- Divide by 4.
Very beginner explanation: Interpreting averages is an important Grade 7 idea in Mean, Median, Mode, Range, and Data Comparisons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 7
Worked Example 4
Problem: Find mean of [20, 25, 30].
- Sum=75.
- Divide by 3.
Very beginner explanation: Interpreting averages is an important Grade 7 idea in Mean, Median, Mode, Range, and Data Comparisons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 25
Worked Example 5
Problem: Find mean of [6, 8, 9, 12, 15].
- Sum=50.
- Divide by 5.
Very beginner explanation: Interpreting averages is an important Grade 7 idea in Mean, Median, Mode, Range, and Data Comparisons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 10
Worked Example 6
Problem: Explain Interpreting averages in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Interpreting averages becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Interpreting averages and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Interpreting averages becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Interpreting averages using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Interpreting averages becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Interpreting averages problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Interpreting averages becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Interpreting averages could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Interpreting averages becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Interpreting averages. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
41.14 Real-life data problems
Data are observations, measurements, or categories collected to answer questions. This topic focuses on Real-life data problems .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Favourite school subject
- Classify it as categorical/qualitative data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Real-life data problems .
Answer: Use a frequency table
Worked Example 2
Problem: Student heights
- Classify it as quantitative continuous data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Real-life data problems .
Answer: Measure in centimetres
Worked Example 3
Problem: Number of siblings
- Classify it as quantitative discrete data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Real-life data problems .
Answer: Count whole numbers
Worked Example 4
Problem: Survey every 10th student
- Classify it as systematic sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Real-life data problems .
Answer: Check that the list order does not create bias
Worked Example 5
Problem: Survey only basketball team members about school sports
- Classify it as biased sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Real-life data problems .
Answer: Broaden the sample
Worked Example 6
Problem: Classify the data [4, 6, 8].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 7
Problem: Classify the data [5, 9, 10, 12].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 8
Problem: Classify the data [3, 7, 7, 11].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 9
Problem: Classify the data [20, 25, 30].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 10
Problem: Classify the data [6, 8, 9, 12, 15].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Practice Exercise
Create one new question about Real-life data problems. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
Chapter Notes, Practice, and Common Mistakes
Chapter Notes
- Read the complete question before choosing an operation, formula, graph, or model.
- Write technical words together with their meaning until you are comfortable using them.
- Show all important steps so another student can follow your reasoning.
- Keep units, labels, signs, axes, variables, and mathematical symbols clear.
- Estimate before or after calculating when an estimate can help check reasonableness.
- For real-life problems, explain what the final number means in the situation.
Extra Practice
- Create and solve a new question about Mean . Show your reasoning and check your answer.
- Create and solve a new question about Median . Show your reasoning and check your answer.
- Create and solve a new question about Mode . Show your reasoning and check your answer.
- Create and solve a new question about Range . Show your reasoning and check your answer.
- Create and solve a new question about Calculating mean . Show your reasoning and check your answer.
- Create and solve a new question about Finding median . Show your reasoning and check your answer.
- Create and solve a new question about Finding mode . Show your reasoning and check your answer.
- Create and solve a new question about Finding range . Show your reasoning and check your answer.
- Create and solve a new question about Outliers . Show your reasoning and check your answer.
- Create and solve a new question about Effect of outliers on mean . Show your reasoning and check your answer.
- Create and solve a new question about Comparing two data sets . Show your reasoning and check your answer.
- Create and solve a new question about Choosing a useful measure . Show your reasoning and check your answer.
Common Mistakes
- Using a biased or unrepresentative sample.
- Reading graph scales incorrectly.
- Treating a misleading graph as trustworthy without checking the axes.
- Assuming dependent events are independent.
- Using percentages in a circle graph that do not total 100%.
30 Review Questions and Answers
Q1. What is important to remember about Mean?
Answer: The mean is the sum of all values divided by the number of values. This topic focuses on Mean.
Q2. What is important to remember about Median?
Answer: The median is the middle value after data are put in order. This topic focuses on Median.
Q3. What is important to remember about Mode?
Answer: The mode is the value that occurs most often. This topic focuses on Mode.
Q4. What is important to remember about Range?
Answer: The range is the greatest value minus the least value. This topic focuses on Range.
Q5. What is important to remember about Calculating mean?
Answer: The mean is the sum of all values divided by the number of values. This topic focuses on Calculating mean.
Q6. What is important to remember about Finding median?
Answer: The median is the middle value after data are put in order. This topic focuses on Finding median.
Q7. What is important to remember about Finding mode?
Answer: The mode is the value that occurs most often. This topic focuses on Finding mode.
Q8. What is important to remember about Finding range?
Answer: The range is the greatest value minus the least value. This topic focuses on Finding range.
Q9. What is important to remember about Outliers?
Answer: Outliers is an important Grade 7 idea in Mean, Median, Mode, Range, and Data Comparisons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q10. What is important to remember about Effect of outliers on mean?
Answer: The mean is the sum of all values divided by the number of values. This topic focuses on Effect of outliers on mean.
Q11. What is important to remember about Comparing two data sets?
Answer: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Comparing two data sets.
Q12. What is important to remember about Choosing a useful measure?
Answer: Choosing a useful measure is an important Grade 7 idea in Mean, Median, Mode, Range, and Data Comparisons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q13. What is important to remember about Interpreting averages?
Answer: Interpreting averages is an important Grade 7 idea in Mean, Median, Mode, Range, and Data Comparisons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q14. What is important to remember about Real-life data problems?
Answer: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Real-life data problems.
Q15. Why should you show your steps?
Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.
Q16. Why is estimation useful?
Answer: Estimation helps you judge whether a final answer is reasonable before accepting it.
Q17. Why do units matter?
Answer: Units tell what a value measures and prevent incompatible quantities from being mixed.
Q18. When should you round?
Answer: Usually round near the end of a calculation unless the question specifically asks for earlier rounding.
Q19. How can you check an answer?
Answer: Use an inverse operation, substitution, estimation, a graph, or a second method.
Q20. What should you identify first in a word problem?
Answer: Identify what is known, what is unknown, and the relationship connecting them.
Q21. What makes a final answer complete?
Answer: Give the value, correct units when needed, and a brief interpretation in context.
Q22. What should you do if an answer seems unreasonable?
Answer: Re-read the question, check copied values, signs, units, formulas, and calculations.
Q23. Why are diagrams useful?
Answer: A labelled diagram can reveal relationships between lengths, angles, areas, and other quantities.
Q24. Why are tables useful?
Answer: Tables organize values and help reveal patterns, relationships, rates, and missing information.
Q25. Why should you explain your reasoning?
Answer: Reasoning shows why a method works, not just what answer you obtained.
Q26. How do mistakes help learning?
Answer: Analyzing a mistake identifies the misunderstood rule or step and helps prevent the same error later.
Q27. How should you study this chapter?
Answer: Review definitions, redo worked examples without looking, practise mixed questions, and explain solutions in your own words.
Q28. When is a calculator useful?
Answer: A calculator is useful for lengthy arithmetic after you understand the mathematical setup and can estimate the expected size of the answer.
Q29. Why compare more than one strategy?
Answer: Different strategies can make a problem easier and provide a way to verify the result.
Q30. What is a mathematical model?
Answer: It is a simplified mathematical representation of a real situation used to analyze, explain, or predict.