Lecture Notes: Calculating Mean, Median, Mode, and Range

Introduction

• Focus on calculating four statistical measures: Mean, Median, Mode, and Range.

Example 1

Data Set: 12, 7, 14, 5, 7, 11, 9

Calculate the Mean (Average)

• Sum of numbers: 12 + 7 + 14 + 5 + 7 + 11 + 9 = 65
• Divide by the count of numbers (7): 65 / 7 = 9.286 (rounded)

Calculate the Median

• Arrange numbers in increasing order: 5, 7, 7, 9, 11, 12, 14
• Middle number: 9

Calculate the Mode

• Number that appears most frequently: 7 appears twice

Calculate the Range

• Difference between the highest and lowest number: 14 - 5 = 9

Example 2

Data Set: 6, 14, 8, 5, 3, 11, 9

Calculate the Mean

• Sum: 6 + 14 + 8 + 5 + 3 + 11 + 9 = 56
• Divide by 7: 56 / 7 = 8

Calculate the Median

• Ordered data: 3, 5, 6, 8, 9, 11, 14
• Middle number: 8

Calculate the Mode

• No number repeats: No mode

Calculate the Range

• Highest number - Lowest number: 14 - 3 = 11

Example 3 (Even Number of Data Points)

Data Set: 6, 8, 5, 5, 9, 8, 10, 8

Calculate the Mean

• Sum: 6 + 8 + 5 + 5 + 9 + 8 + 10 + 8 = 59
• Divide by 8: 59 / 8 = 7.375

Calculate the Mode

• Most frequent number: 8 appears thrice

Calculate the Median

• Ordered data: 5, 5, 6, 8, 8, 8, 9, 10
• Middle numbers: 8 and 8, so median is 8

Calculate the Range

• Highest - Lowest: 10 - 5 = 5

Example 4 (10 Numbers)

Data Set: 12, 15, 21, 4, 36, 15, 11, 48, 29, 38

Calculate the Mean

• Sum: 229
• Divide by 10: 229 / 10 = 22.9

Calculate the Median

• Ordered: 4, 11, 12, 15, 15, 21, 29, 36, 38, 48
• Middle numbers: 15 and 21
• Average of middle numbers: (15 + 21) / 2 = 18

Calculate the Mode

• Most frequent number: 15 appears twice

Calculate the Range

• Highest - Lowest: 48 - 4 = 44

Conclusion

• Methodology applied to different data sets to find mean, median, mode, and range effectively.