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Chapter 53: Mean, Median, Mode, Range, and Outliers

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

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

This chapter contains 13 topics. Technical terms are followed by plain-language meanings where they first appear. Each topic includes at least five worked examples. Coding is included only where it naturally supports the Grade 8 coding expectations.

53.1 Mean

The mean is the sum of all values divided by the number of values. In this section, the focus is Mean.

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

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

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

  1. Add the values: 18.
  2. Divide by 3.

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

Answer: 6

Worked Example 2

Problem: Find the mean of [5, 9, 10, 12].

  1. Add the values: 36.
  2. Divide by 4.

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

Answer: 9

Worked Example 3

Problem: Find the mean of [3, 7, 7, 11].

  1. Add the values: 28.
  2. Divide by 4.

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

Answer: 7

Worked Example 4

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

  1. Add the values: 75.
  2. Divide by 3.

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

Answer: 25

Worked Example 5

Problem: Find the mean of [6, 8, 9, 12, 15].

  1. Add the values: 50.
  2. Divide by 5.

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

Answer: 10

Worked Example 6

Problem: Find the mean of [2, 4, 4, 5, 20].

  1. Add the values: 35.
  2. Divide by 5.

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

Answer: 7

Worked Example 7

Problem: Find the mean of [10, 11, 12, 13, 14].

  1. Add the values: 60.
  2. Divide by 5.

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

Answer: 12

Worked Example 8

Problem: Find the mean of [1, 3, 5, 7, 9].

  1. Add the values: 25.
  2. Divide by 5.

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

Answer: 5

Worked Example 9

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

  1. Add the values: 43.
  2. Divide by 5.

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

Answer: 8.6

Worked Example 10

Problem: Find the mean of [15, 18, 21, 24, 27].

  1. Add the values: 105.
  2. Divide by 5.

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

Answer: 21

Practice exercise

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

53.2 Median

The median is the middle value after data are put in order. In this section, the focus is Median.

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

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

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

  1. Order the values.
  2. Choose the middle value; if there are two middle values, average them.

Very beginner explanation: Median depends on position after sorting, not on the total sum.

Answer: 6

Worked Example 2

Problem: Find the median of [5, 9, 10, 12].

  1. Order the values.
  2. Choose the middle value; if there are two middle values, average them.

Very beginner explanation: Median depends on position after sorting, not on the total sum.

Answer: 9.5

Worked Example 3

Problem: Find the median of [3, 7, 7, 11].

  1. Order the values.
  2. Choose the middle value; if there are two middle values, average them.

Very beginner explanation: Median depends on position after sorting, not on the total sum.

Answer: 7

Worked Example 4

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

  1. Order the values.
  2. Choose the middle value; if there are two middle values, average them.

Very beginner explanation: Median depends on position after sorting, not on the total sum.

Answer: 25

Worked Example 5

Problem: Find the median of [6, 8, 9, 12, 15].

  1. Order the values.
  2. Choose the middle value; if there are two middle values, average them.

Very beginner explanation: Median depends on position after sorting, not on the total sum.

Answer: 9

Worked Example 6

Problem: Find the median of [2, 4, 4, 5, 20].

  1. Order the values.
  2. Choose the middle value; if there are two middle values, average them.

Very beginner explanation: Median depends on position after sorting, not on the total sum.

Answer: 4

Worked Example 7

Problem: Find the median of [10, 11, 12, 13, 14].

  1. Order the values.
  2. Choose the middle value; if there are two middle values, average them.

Very beginner explanation: Median depends on position after sorting, not on the total sum.

Answer: 12

Worked Example 8

Problem: Find the median of [1, 3, 5, 7, 9].

  1. Order the values.
  2. Choose the middle value; if there are two middle values, average them.

Very beginner explanation: Median depends on position after sorting, not on the total sum.

Answer: 5

Worked Example 9

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

  1. Order the values.
  2. Choose the middle value; if there are two middle values, average them.

Very beginner explanation: Median depends on position after sorting, not on the total sum.

Answer: 8

Worked Example 10

Problem: Find the median of [15, 18, 21, 24, 27].

  1. Order the values.
  2. Choose the middle value; if there are two middle values, average them.

Very beginner explanation: Median depends on position after sorting, not on the total sum.

Answer: 21

Practice exercise

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

53.3 Mode

The mode is the value that occurs most often. In this section, the focus is Mode.

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

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

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

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value; a set can have no mode or more than one mode.

Answer: No mode

Worked Example 2

Problem: Find the mode of [5, 9, 10, 12].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value; a set can have no mode or more than one mode.

Answer: No mode

Worked Example 3

Problem: Find the mode of [3, 7, 7, 11].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value; a set can have no mode or more than one mode.

Answer: 7

Worked Example 4

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

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value; a set can have no mode or more than one mode.

Answer: No mode

Worked Example 5

Problem: Find the mode of [6, 8, 9, 12, 15].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value; a set can have no mode or more than one mode.

Answer: No mode

Worked Example 6

Problem: Find the mode of [2, 4, 4, 5, 20].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value; a set can have no mode or more than one mode.

Answer: 4

Worked Example 7

Problem: Find the mode of [10, 11, 12, 13, 14].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value; a set can have no mode or more than one mode.

Answer: No mode

Worked Example 8

Problem: Find the mode of [1, 3, 5, 7, 9].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value; a set can have no mode or more than one mode.

Answer: No mode

Worked Example 9

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

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value; a set can have no mode or more than one mode.

Answer: 8

Worked Example 10

Problem: Find the mode of [15, 18, 21, 24, 27].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value; a set can have no mode or more than one mode.

Answer: No mode

Practice exercise

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

53.4 Range

The range is the greatest value minus the least value. In this section, the focus is Range.

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

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

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

  1. Find the greatest value.
  2. Find the least value.
  3. Subtract least from greatest.

Very beginner explanation: Range is a simple measure of spread.

Answer: 4

Worked Example 2

Problem: Find the range of [5, 9, 10, 12].

  1. Find the greatest value.
  2. Find the least value.
  3. Subtract least from greatest.

Very beginner explanation: Range is a simple measure of spread.

Answer: 7

Worked Example 3

Problem: Find the range of [3, 7, 7, 11].

  1. Find the greatest value.
  2. Find the least value.
  3. Subtract least from greatest.

Very beginner explanation: Range is a simple measure of spread.

Answer: 8

Worked Example 4

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

  1. Find the greatest value.
  2. Find the least value.
  3. Subtract least from greatest.

Very beginner explanation: Range is a simple measure of spread.

Answer: 10

Worked Example 5

Problem: Find the range of [6, 8, 9, 12, 15].

  1. Find the greatest value.
  2. Find the least value.
  3. Subtract least from greatest.

Very beginner explanation: Range is a simple measure of spread.

Answer: 9

Worked Example 6

Problem: Find the range of [2, 4, 4, 5, 20].

  1. Find the greatest value.
  2. Find the least value.
  3. Subtract least from greatest.

Very beginner explanation: Range is a simple measure of spread.

Answer: 18

Worked Example 7

Problem: Find the range of [10, 11, 12, 13, 14].

  1. Find the greatest value.
  2. Find the least value.
  3. Subtract least from greatest.

Very beginner explanation: Range is a simple measure of spread.

Answer: 4

Worked Example 8

Problem: Find the range of [1, 3, 5, 7, 9].

  1. Find the greatest value.
  2. Find the least value.
  3. Subtract least from greatest.

Very beginner explanation: Range is a simple measure of spread.

Answer: 8

Worked Example 9

Problem: Find the range of [8, 8, 8, 9, 10].

  1. Find the greatest value.
  2. Find the least value.
  3. Subtract least from greatest.

Very beginner explanation: Range is a simple measure of spread.

Answer: 2

Worked Example 10

Problem: Find the range of [15, 18, 21, 24, 27].

  1. Find the greatest value.
  2. Find the least value.
  3. Subtract least from greatest.

Very beginner explanation: Range is a simple measure of spread.

Answer: 12

Practice exercise

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

53.5 Calculating mean

The mean is the sum of all values divided by the number of values. In this section, the focus is Calculating mean.

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

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

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

  1. Add the values: 18.
  2. Divide by 3.

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

Answer: 6

Worked Example 2

Problem: Find the mean of [5, 9, 10, 12].

  1. Add the values: 36.
  2. Divide by 4.

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

Answer: 9

Worked Example 3

Problem: Find the mean of [3, 7, 7, 11].

  1. Add the values: 28.
  2. Divide by 4.

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

Answer: 7

Worked Example 4

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

  1. Add the values: 75.
  2. Divide by 3.

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

Answer: 25

Worked Example 5

Problem: Find the mean of [6, 8, 9, 12, 15].

  1. Add the values: 50.
  2. Divide by 5.

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

Answer: 10

Worked Example 6

Problem: Find the mean of [2, 4, 4, 5, 20].

  1. Add the values: 35.
  2. Divide by 5.

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

Answer: 7

Worked Example 7

Problem: Find the mean of [10, 11, 12, 13, 14].

  1. Add the values: 60.
  2. Divide by 5.

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

Answer: 12

Worked Example 8

Problem: Find the mean of [1, 3, 5, 7, 9].

  1. Add the values: 25.
  2. Divide by 5.

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

Answer: 5

Worked Example 9

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

  1. Add the values: 43.
  2. Divide by 5.

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

Answer: 8.6

Worked Example 10

Problem: Find the mean of [15, 18, 21, 24, 27].

  1. Add the values: 105.
  2. Divide by 5.

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

Answer: 21

Practice exercise

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

53.6 Finding median

The median is the middle value after data are put in order. In this section, the focus is Finding median.

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

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

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

  1. Order the values.
  2. Choose the middle value; if there are two middle values, average them.

Very beginner explanation: Median depends on position after sorting, not on the total sum.

Answer: 6

Worked Example 2

Problem: Find the median of [5, 9, 10, 12].

  1. Order the values.
  2. Choose the middle value; if there are two middle values, average them.

Very beginner explanation: Median depends on position after sorting, not on the total sum.

Answer: 9.5

Worked Example 3

Problem: Find the median of [3, 7, 7, 11].

  1. Order the values.
  2. Choose the middle value; if there are two middle values, average them.

Very beginner explanation: Median depends on position after sorting, not on the total sum.

Answer: 7

Worked Example 4

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

  1. Order the values.
  2. Choose the middle value; if there are two middle values, average them.

Very beginner explanation: Median depends on position after sorting, not on the total sum.

Answer: 25

Worked Example 5

Problem: Find the median of [6, 8, 9, 12, 15].

  1. Order the values.
  2. Choose the middle value; if there are two middle values, average them.

Very beginner explanation: Median depends on position after sorting, not on the total sum.

Answer: 9

Worked Example 6

Problem: Find the median of [2, 4, 4, 5, 20].

  1. Order the values.
  2. Choose the middle value; if there are two middle values, average them.

Very beginner explanation: Median depends on position after sorting, not on the total sum.

Answer: 4

Worked Example 7

Problem: Find the median of [10, 11, 12, 13, 14].

  1. Order the values.
  2. Choose the middle value; if there are two middle values, average them.

Very beginner explanation: Median depends on position after sorting, not on the total sum.

Answer: 12

Worked Example 8

Problem: Find the median of [1, 3, 5, 7, 9].

  1. Order the values.
  2. Choose the middle value; if there are two middle values, average them.

Very beginner explanation: Median depends on position after sorting, not on the total sum.

Answer: 5

Worked Example 9

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

  1. Order the values.
  2. Choose the middle value; if there are two middle values, average them.

Very beginner explanation: Median depends on position after sorting, not on the total sum.

Answer: 8

Worked Example 10

Problem: Find the median of [15, 18, 21, 24, 27].

  1. Order the values.
  2. Choose the middle value; if there are two middle values, average them.

Very beginner explanation: Median depends on position after sorting, not on the total sum.

Answer: 21

Practice exercise

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

53.7 Finding mode

The mode is the value that occurs most often. In this section, the focus is Finding mode.

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

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

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

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value; a set can have no mode or more than one mode.

Answer: No mode

Worked Example 2

Problem: Find the mode of [5, 9, 10, 12].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value; a set can have no mode or more than one mode.

Answer: No mode

Worked Example 3

Problem: Find the mode of [3, 7, 7, 11].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value; a set can have no mode or more than one mode.

Answer: 7

Worked Example 4

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

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value; a set can have no mode or more than one mode.

Answer: No mode

Worked Example 5

Problem: Find the mode of [6, 8, 9, 12, 15].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value; a set can have no mode or more than one mode.

Answer: No mode

Worked Example 6

Problem: Find the mode of [2, 4, 4, 5, 20].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value; a set can have no mode or more than one mode.

Answer: 4

Worked Example 7

Problem: Find the mode of [10, 11, 12, 13, 14].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value; a set can have no mode or more than one mode.

Answer: No mode

Worked Example 8

Problem: Find the mode of [1, 3, 5, 7, 9].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value; a set can have no mode or more than one mode.

Answer: No mode

Worked Example 9

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

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value; a set can have no mode or more than one mode.

Answer: 8

Worked Example 10

Problem: Find the mode of [15, 18, 21, 24, 27].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value; a set can have no mode or more than one mode.

Answer: No mode

Practice exercise

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

53.8 Finding range

The range is the greatest value minus the least value. In this section, the focus is Finding range.

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

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

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

  1. Find the greatest value.
  2. Find the least value.
  3. Subtract least from greatest.

Very beginner explanation: Range is a simple measure of spread.

Answer: 4

Worked Example 2

Problem: Find the range of [5, 9, 10, 12].

  1. Find the greatest value.
  2. Find the least value.
  3. Subtract least from greatest.

Very beginner explanation: Range is a simple measure of spread.

Answer: 7

Worked Example 3

Problem: Find the range of [3, 7, 7, 11].

  1. Find the greatest value.
  2. Find the least value.
  3. Subtract least from greatest.

Very beginner explanation: Range is a simple measure of spread.

Answer: 8

Worked Example 4

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

  1. Find the greatest value.
  2. Find the least value.
  3. Subtract least from greatest.

Very beginner explanation: Range is a simple measure of spread.

Answer: 10

Worked Example 5

Problem: Find the range of [6, 8, 9, 12, 15].

  1. Find the greatest value.
  2. Find the least value.
  3. Subtract least from greatest.

Very beginner explanation: Range is a simple measure of spread.

Answer: 9

Worked Example 6

Problem: Find the range of [2, 4, 4, 5, 20].

  1. Find the greatest value.
  2. Find the least value.
  3. Subtract least from greatest.

Very beginner explanation: Range is a simple measure of spread.

Answer: 18

Worked Example 7

Problem: Find the range of [10, 11, 12, 13, 14].

  1. Find the greatest value.
  2. Find the least value.
  3. Subtract least from greatest.

Very beginner explanation: Range is a simple measure of spread.

Answer: 4

Worked Example 8

Problem: Find the range of [1, 3, 5, 7, 9].

  1. Find the greatest value.
  2. Find the least value.
  3. Subtract least from greatest.

Very beginner explanation: Range is a simple measure of spread.

Answer: 8

Worked Example 9

Problem: Find the range of [8, 8, 8, 9, 10].

  1. Find the greatest value.
  2. Find the least value.
  3. Subtract least from greatest.

Very beginner explanation: Range is a simple measure of spread.

Answer: 2

Worked Example 10

Problem: Find the range of [15, 18, 21, 24, 27].

  1. Find the greatest value.
  2. Find the least value.
  3. Subtract least from greatest.

Very beginner explanation: Range is a simple measure of spread.

Answer: 12

Practice exercise

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

53.9 Outliers

Outliers is an important Grade 8 concept in Mean, Median, Mode, Range, and Outliers. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

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

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

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

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

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

Answer: Quantitative data

Worked Example 2

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

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

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

Answer: Quantitative data

Worked Example 3

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

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

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

Answer: Quantitative data

Worked Example 4

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

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

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

Answer: Quantitative data

Worked Example 5

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

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

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

Answer: Quantitative data

Worked Example 6

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

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

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

Answer: Quantitative data

Worked Example 7

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

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

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

Answer: Quantitative data

Worked Example 8

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

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

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

Answer: Quantitative data

Worked Example 9

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

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

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

Answer: Quantitative data

Worked Example 10

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

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

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

Answer: Quantitative data

Practice exercise

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

53.10 Effect of outliers on mean

The mean is the sum of all values divided by the number of values. In this section, the focus is Effect of outliers on mean.

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

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

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

  1. Add the values: 18.
  2. Divide by 3.

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

Answer: 6

Worked Example 2

Problem: Find the mean of [5, 9, 10, 12].

  1. Add the values: 36.
  2. Divide by 4.

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

Answer: 9

Worked Example 3

Problem: Find the mean of [3, 7, 7, 11].

  1. Add the values: 28.
  2. Divide by 4.

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

Answer: 7

Worked Example 4

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

  1. Add the values: 75.
  2. Divide by 3.

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

Answer: 25

Worked Example 5

Problem: Find the mean of [6, 8, 9, 12, 15].

  1. Add the values: 50.
  2. Divide by 5.

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

Answer: 10

Worked Example 6

Problem: Find the mean of [2, 4, 4, 5, 20].

  1. Add the values: 35.
  2. Divide by 5.

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

Answer: 7

Worked Example 7

Problem: Find the mean of [10, 11, 12, 13, 14].

  1. Add the values: 60.
  2. Divide by 5.

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

Answer: 12

Worked Example 8

Problem: Find the mean of [1, 3, 5, 7, 9].

  1. Add the values: 25.
  2. Divide by 5.

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

Answer: 5

Worked Example 9

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

  1. Add the values: 43.
  2. Divide by 5.

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

Answer: 8.6

Worked Example 10

Problem: Find the mean of [15, 18, 21, 24, 27].

  1. Add the values: 105.
  2. Divide by 5.

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

Answer: 21

Practice exercise

Create one new Grade 8 problem involving Effect of outliers on mean. Show the important steps, include units when needed, and explain how you checked the answer.

53.11 Effect of outliers on median

The median is the middle value after data are put in order. In this section, the focus is Effect of outliers on median.

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

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

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

  1. Order the values.
  2. Choose the middle value; if there are two middle values, average them.

Very beginner explanation: Median depends on position after sorting, not on the total sum.

Answer: 6

Worked Example 2

Problem: Find the median of [5, 9, 10, 12].

  1. Order the values.
  2. Choose the middle value; if there are two middle values, average them.

Very beginner explanation: Median depends on position after sorting, not on the total sum.

Answer: 9.5

Worked Example 3

Problem: Find the median of [3, 7, 7, 11].

  1. Order the values.
  2. Choose the middle value; if there are two middle values, average them.

Very beginner explanation: Median depends on position after sorting, not on the total sum.

Answer: 7

Worked Example 4

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

  1. Order the values.
  2. Choose the middle value; if there are two middle values, average them.

Very beginner explanation: Median depends on position after sorting, not on the total sum.

Answer: 25

Worked Example 5

Problem: Find the median of [6, 8, 9, 12, 15].

  1. Order the values.
  2. Choose the middle value; if there are two middle values, average them.

Very beginner explanation: Median depends on position after sorting, not on the total sum.

Answer: 9

Worked Example 6

Problem: Find the median of [2, 4, 4, 5, 20].

  1. Order the values.
  2. Choose the middle value; if there are two middle values, average them.

Very beginner explanation: Median depends on position after sorting, not on the total sum.

Answer: 4

Worked Example 7

Problem: Find the median of [10, 11, 12, 13, 14].

  1. Order the values.
  2. Choose the middle value; if there are two middle values, average them.

Very beginner explanation: Median depends on position after sorting, not on the total sum.

Answer: 12

Worked Example 8

Problem: Find the median of [1, 3, 5, 7, 9].

  1. Order the values.
  2. Choose the middle value; if there are two middle values, average them.

Very beginner explanation: Median depends on position after sorting, not on the total sum.

Answer: 5

Worked Example 9

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

  1. Order the values.
  2. Choose the middle value; if there are two middle values, average them.

Very beginner explanation: Median depends on position after sorting, not on the total sum.

Answer: 8

Worked Example 10

Problem: Find the median of [15, 18, 21, 24, 27].

  1. Order the values.
  2. Choose the middle value; if there are two middle values, average them.

Very beginner explanation: Median depends on position after sorting, not on the total sum.

Answer: 21

Practice exercise

Create one new Grade 8 problem involving Effect of outliers on median. Show the important steps, include units when needed, and explain how you checked the answer.

53.12 Comparing data sets

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

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

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

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

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

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

Answer: Quantitative data

Worked Example 2

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

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

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

Answer: Quantitative data

Worked Example 3

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

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

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

Answer: Quantitative data

Worked Example 4

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

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

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

Answer: Quantitative data

Worked Example 5

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

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

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

Answer: Quantitative data

Worked Example 6

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

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

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

Answer: Quantitative data

Worked Example 7

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

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

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

Answer: Quantitative data

Worked Example 8

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

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

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

Answer: Quantitative data

Worked Example 9

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

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

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

Answer: Quantitative data

Worked Example 10

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

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

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

Answer: Quantitative data

Practice exercise

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

53.13 Choosing an appropriate measure

Choosing an appropriate measure is an important Grade 8 concept in Mean, Median, Mode, Range, and Outliers. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

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

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

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

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

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

Answer: Quantitative data

Worked Example 2

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

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

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

Answer: Quantitative data

Worked Example 3

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

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

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

Answer: Quantitative data

Worked Example 4

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

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

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

Answer: Quantitative data

Worked Example 5

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

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

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

Answer: Quantitative data

Worked Example 6

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

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

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

Answer: Quantitative data

Worked Example 7

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

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

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

Answer: Quantitative data

Worked Example 8

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

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

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

Answer: Quantitative data

Worked Example 9

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

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

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

Answer: Quantitative data

Worked Example 10

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

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

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

Answer: Quantitative data

Practice exercise

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

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Chapter 53 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. In this section, the focus is Mean.

Q2. What is important to remember about Median?

Answer: The median is the middle value after data are put in order. In this section, the focus is Median.

Q3. What is important to remember about Mode?

Answer: The mode is the value that occurs most often. In this section, the focus is Mode.

Q4. What is important to remember about Range?

Answer: The range is the greatest value minus the least value. In this section, the focus is 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. In this section, the focus is Calculating mean.

Q6. What is important to remember about Finding median?

Answer: The median is the middle value after data are put in order. In this section, the focus is Finding median.

Q7. What is important to remember about Finding mode?

Answer: The mode is the value that occurs most often. In this section, the focus is Finding mode.

Q8. What is important to remember about Finding range?

Answer: The range is the greatest value minus the least value. In this section, the focus is Finding range.

Q9. What is important to remember about Outliers?

Answer: Outliers is an important Grade 8 concept in Mean, Median, Mode, Range, and Outliers. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

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. In this section, the focus is Effect of outliers on mean.

Q11. What is important to remember about Effect of outliers on median?

Answer: The median is the middle value after data are put in order. In this section, the focus is Effect of outliers on median.

Q12. What is important to remember about Comparing data sets?

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

Q13. What is important to remember about Choosing an appropriate measure?

Answer: Choosing an appropriate measure is an important Grade 8 concept in Mean, Median, Mode, Range, and Outliers. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q14. Why should you show your steps?

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

Q15. Why is estimation useful?

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

Q16. Why do units matter?

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

Q17. When should you round?

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

Q18. How can you check an answer?

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

Q19. What should you identify first in a word problem?

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

Q20. What makes a final answer complete?

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

Q21. What should you do if an answer seems unreasonable?

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

Q22. Why are diagrams useful?

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

Q23. Why are tables useful?

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

Q24. Why should you explain your reasoning?

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

Q25. How do mistakes help learning?

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

Q26. When is a calculator useful?

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

Q27. Why compare more than one strategy?

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

Q28. What is mathematical communication?

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

Q29. What is mathematical modelling?

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

Q30. Why should assumptions be stated?

Answer: Assumptions show the conditions the model depends on and help readers judge whether it is reasonable.