Introduction to Mean, Median, and Mode

Grade 5 Medium Probability & Statistics

Learning Objectives

  • Calculate the mean (average) of a data set
  • Find the median (middle value) of a data set
  • Identify the mode (most frequent value) of a data set

Concept Explanation

Measures of central tendency are values that represent the center or typical value of a data set. The three main measures are:

  1. Mean: The average of all values, calculated by adding all numbers and dividing by how many there are.

    • Formula: Mean = (Sum of all values) ÷ (Number of values)

  2. Median: The middle value when all numbers are arranged in order.

    • For an odd number of values: The middle number
    • For an even number of values: The average of the two middle numbers

  3. Mode: The value that appears most frequently in the data set.

    • A data set can have one mode, multiple modes, or no mode

Each measure provides different insights about the data and can be affected differently by outliers (extreme values).

Worked Examples

Example 1

Problem: Find the mean, median, and mode of: 4, 7, 10, 7, 12
Solution:
Mean: 8
Median: 7
Mode: 7
Explanation:
Mean: (4 + 7 + 10 + 7 + 12) ÷ 5 = 40 ÷ 5 = 8
Median: Arrange in order: 4, 7, 7, 10, 12. The middle value is 7.
Mode: 7 appears twice, while other values appear only once.

Example 2

Problem: Find the mean, median, and mode of: 15, 18, 12, 22, 15, 19
Solution:
Mean: 16.83
Median: 16.5
Mode: 15
Explanation:
Mean: (15 + 18 + 12 + 22 + 15 + 19) ÷ 6 = 101 ÷ 6 = 16.83
Median: Arrange in order: 12, 15, 15, 18, 19, 22. The middle values are 15 and 18, so (15 + 18) ÷ 2 = 16.5
Mode: 15 appears twice, while other values appear only once.

Example 3

Problem: Find the mean, median, and mode of: 5, 5, 5, 5, 5
Solution:
Mean: 5
Median: 5
Mode: 5
Explanation:
Mean: (5 + 5 + 5 + 5 + 5) ÷ 5 = 25 ÷ 5 = 5
Median: All values are 5, so the middle value is 5.
Mode: All values are 5, so the mode is 5.

Common Errors

ErrorCorrectionReason
Forgetting to order values for medianAlways arrange numbers in ascending order firstThe median must be calculated from an ordered list.
Miscounting when finding the meanDouble-check the count of values in the denominatorUsing the wrong count leads to an incorrect average.
Confusing no mode with one modeRemember a value must appear more than once to be a modeIf all values appear equally often, there is no mode.

Practice Problems

  1. Problem: Find the mean of: 12, 15, 18, 21, 24
    Solution: 18
  2. Problem: Find the median of: 7, 3, 9, 5, 1, 8
    Solution: 6
  3. Problem: Find the mode of: 4, 2, 7, 2, 8, 2, 9
    Solution: 2
  4. Problem: Find the mean, median, and mode of: 6, 8, 10, 8, 6
    Solution: Mean: 7.6, Median: 8, Mode: 6 and 8
  5. Problem: Find the median of: 15, 22, 17, 19, 20
    Solution: 19

Real-World Application Example

Measures of central tendency are used extensively in real life. Teachers use the mean to calculate average test scores, meteorologists use the median to report typical rainfall (since it’s less affected by extreme weather events), and retailers track the mode to identify their most popular products. Understanding these concepts helps us interpret data in news reports, scientific studies, and everyday decision-making.

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