Lecture on Cumulative Frequency Diagrams

Introduction

• Topic: Cumulative Frequency Diagrams
• Example Context: Test marks scored by students in an exam.

Cumulative Frequency Table

• Initial Step: First entry is the same as the regular frequency table.
• Process:
  • Copy the first entry from the regular frequency table.
  • For the next entries, add the frequency of the current interval to the cumulative sum of previous frequencies.
  • Continue till the end of the table.

Example

• 0 to 20 marks: Frequency = 6
• 20 to 40 marks: Add 22 (from this interval) to previous cumulative frequency (6) to get 28.
• 40 to 60 marks: Add 36 to 28 to get 64.
• 60 to 80 marks: Add 45 to 64 to get 109.
• 80 to 100 marks: Add 11 to 109 to get 120.

Cumulative Frequency Diagram

• Axes Setup:
  • Horizontal axis: Test marks (0 to 100).
  • Vertical axis: Cumulative frequency (up to 120).
• Plotting Points:
  • Plot points at the end of each interval.
  • Example: At 20 marks, plot frequency of 6.
• Connecting Points:
  • Use either straight lines or a smooth curve.
  • Recommendation: Use straight lines for simplicity.

Reading and Interpreting Diagrams

Calculating the Median

• Determine total frequency: Read the highest point on the diagram.
• Locate Median:
  • Find half of total cumulative frequency.
  • Draw line across at this half value until it hits the curve and read the corresponding mark.

Interquartile Range

• Lower Quartile:
  • Find 1/4 of the total frequency and read the corresponding mark.
• Upper Quartile:
  • Find 3/4 of the total frequency and read the corresponding mark.
• Interquartile Range: Subtract lower quartile value from upper quartile value.

Probability and Frequency Calculations

• Example Problem: Determine the percentage or probability of an event (e.g., students receiving detention).
• Steps:
  • Determine cumulative frequency for a particular time or interval.
  • Use total frequency to calculate relative frequency or percentage.
  • Example: Students more than 5 minutes late.
    • Calculate frequency above 5 minutes.
    • Convert to percentage.

Practice Example

• Scenario: Time spent waiting for a meal at a restaurant.
• Calculate Median and Interquartile Range:
  • Follow similar steps: Find total frequency, median, and interquartile range.

Probability Question

• Example: Determine probability of waiting between 50 and 70 minutes.
• Process:
  • Determine cumulative frequencies at both ends (50 and 70 minutes).
  • Subtract to find frequency in range.
  • Express as a fraction of total frequency for probability.

Conclusion

• Review the process of constructing and interpreting cumulative frequency diagrams through examples.
• Encourage practice with exam questions provided.

• Recommendation: Subscribe for more content and try the practice questions linked in the video.