Math Lecture: Mean, Median, Mode, and Range

Introduction

• Purpose: Understanding how mean, median, mode, and range help analyze data.
• Importance: These metrics provide more information about data, helping better understand it.

Ordering Data

• First Step: Order data from least to greatest.
• Example: Data is already ordered in the example provided.

Mean

• Definition: The average of the data set.
• Calculation Steps:
  1. Add all numbers in the data set to find the sum.
  2. Divide the sum by the number of data points.
• Example:
  • Sum: 72 + 73 + 79 + ... = 753.
  • Number of data points: 9.
  • Calculation: 753 / 9 = 83.666...
  • Result: Rounding to the nearest hundredth gives 83.67.

Median

• Definition: The middle number in an ordered data set.
• Odd Number of Data Points:
  • Middle number is the exact middle.
  • Example: 9 numbers, middle is 5th (84).
• Even Number of Data Points:
  • Average of two middle numbers.
• Resource: More examples provided in a link for median with an even number of data points.

Mode

• Definition: The number that occurs most frequently.
• Example:
  • Data: Two 90s, Three 84s, others are unique.
  • Result: Mode is 84.
• Multiple Modes: Possible if multiple numbers appear with the same highest frequency.
  • Example: 3 occurrences each of 84 and 90 would result in two modes.

Range

• Definition: Measurement of how spread out the data is.
• Calculation:
  • Subtract the smallest number from the largest number.
  • Example: 97 (largest) - 72 (smallest) = 25.
• Result: Range is 25.

Conclusion

• Overview of how to calculate mean, median, mode, and range.
• Additional resources: Links provided for more help or examples.
• Closing: Encouragement to explore the additional links for further understanding.