Mean, Median, and Mode

Introduction

• Three important mathematical concepts: Mean, Median, and Mode.
• Used to analyze data sets (collections of numbers).
• Data sets can be small (e.g., family ages) or large (e.g., store item costs, animal speeds).
• Helps understand and summarize large amounts of data.

Mean (Average)

• Mean and average are the same.
• Represents a consistent value across all numbers in a data set.

Calculating the Mean

1. Add all numbers in the data set.
   • Example with numbers: 1, 8, 3, 2, 6 → Total = 20
2. Divide the total by the number of values.
   • For 5 numbers, 20 ÷ 5 = 4.
   • Example with family ages: Total = 222 years; Mean = 222 ÷ 6 = 37.

Median

• The middle value that splits the data set into two equal halves.
• Requires data to be in order (least to greatest).

Finding the Median

• Odd number of elements: Identify the middle number directly.
  • Example: For {1, 2, 3}, Median = 2.
• Even number of elements: Average the two middle numbers.
  • Example: For {1, 2, 3, 4}, Median = (2 + 3) ÷ 2 = 2.5.

Mean vs. Median

• Sometimes Mean and Median are the same, sometimes they are different.
• Example comparison:
  • Set {1, 2, 3}: Mean = 2, Median = 2.
  • Set {1, 2, 4}: Mean = 2.33, Median = 2.

Mode

• The value that occurs most often in a data set.
• A data set can have:
  • No Mode (all values unique)
  • One Mode (one value repeats most)
  • Multiple Modes (more than one value repeats the same maximum number of times).

Finding the Mode

• Example: In {1, 2, 2, 3, 3, 3}, Mode = 3.
• Example with multiple modes: {7, 15, 15, 7} → Modes = 7 and 15.

Real-World Example: Electric Guitars

• Data Set: Monthly sales of guitars.
• Mean Calculation: Total = 108; Mean = 108 ÷ 12 = 9.
• Median Calculation: Sorted set → Middle values (9 and 10); Median = (9 + 10) ÷ 2 = 9.5.
• Mode Calculation: Most frequent number is 10 (occurs 3 times).

Summary

• Mean: Average value.
• Median: Middle value.
• Mode: Most frequently occurring value.
• Remember: "Mean means average", "Median is in the middle", and "Mode is Most Often".
• Importance of practice in mastering math concepts.