How to Calculate the Mean of a Group Frequency Table

Introduction

• Discussing how to calculate mean using a group frequency table.
• Example: Grades of students with intervals like 40-49, 50-59, etc.
• Grade intervals:
  • 40 to 49: F
  • 50 to 59: F
  • 60 to 69: D
  • 70 to 79: C
  • 80 to 89: B
  • 90 to 100: A
• Frequency column shows number of students in each range.

Calculating the Mean

1. Understanding the Problem

   • We cannot compute an exact mean due to lack of individual data values.
   • Instead, we estimate the mean using grouped data.

2. Formula for Mean in a Group Frequency Table

   • Mean = Sum of (Frequency * Midpoint) / Sum of Frequency.
   • Midpoint of interval = (Lower boundary + Upper boundary) / 2.

3. Calculate Midpoints

   • Example calculation:
     • Interval 40-49: Midpoint = (40 + 49) / 2 = 44.5
     • Interval 50-59: Midpoint = (50 + 59) / 2 = 54.5
     • Pattern: Increments of 10 in midpoints for following intervals.

4. Calculate Sum of Frequencies

   • Sum = 3 + 5 + 6 + 9 + 8 + 7 = 38 (total students).

5. Calculate Sum of Frequency * Midpoint (f * m)

   • Create a column for f * m and calculate:
     • 3 * 44.5 = 133.5
     • 5 * 54.5 = 272.5
     • Continue for other intervals.
   • Total = 2804.5

6. Calculate Mean

   • Mean = 2804.5 / 38 = 73.8
   • Mean is likely in interval 70-79 based on highest frequency.

Median and Mode

• Mode: Interval with highest frequency (70-79).
• Median: Use cumulative frequency to find:
  • Cumulative frequency column calculations.
  • Median occurs where cumulative frequency reaches half of total students.
  • Median in interval 70-79.

Additional Example: Weights of Students

1. Cumulative Frequency

   • 6, 14, 26, 33, 36.

2. Midpoint Calculations

   • E.g., (Upper boundary + Lower boundary) / 2.
   • Intervals: 129.5, 149.5, 169.5, etc.

3. Frequency * Midpoint Calculations

   • E.g., 6 * 129.5 = 777, etc.
   • Total = 5963.5

4. Determine Mean

   • Mean = 5963.5 / 36 = 165.7
   • Majority of data is between 160-179, mean reflects this.

5. Identify Median and Mode

   • Mode: Highest frequency interval (160-179).
   • Median: 18th student located in interval 160-179.

Conclusion

• The process includes determining midpoints, calculating f * m, and understanding position of median and mode.
• Practice with different datasets to reinforce understanding.*