Understanding Percentile Rank

Definition of Percentile Rank

• Percentile Rank: The point in a distribution where a percentage of scores are below a particular score.
• Example: If a score of 75 has a rank of 60, it means 60% of the scores are below 75.

Steps to Solve the Percentile Rank of Ungrouped Data

Step 1: Analyze the Scores

• Identify the range of scores and what is being sought.
• Example: Determine the rank of the score 18 from the range: 20, 8, 7, 15, 5, 10, 18, and 25.

Step 2: Arrange the Data

• Sort the scores from lowest to highest.
• Order: 5, 7, 8, 10, 15, 18, 20, 25.

Step 3: Solve the Percentile Rank

• Use the formula:
  • Percent Rank = (Cumulative Frequency + 0.5 * Frequency) / n * 100
  • CF (Cumulative Frequency): Number of scores less than the specified score.
  • F (Frequency): Number of occurrences of the specified score.
  • n: Total number of scores.

Step 4: Substitute the Values

• Identify CF: Number of scores less than 18 is 5.
• Identify F: The score 18 appears once, so F = 1.
• The total scores, n = 8.

Step 5: Solution

• Substitute the values into the formula:
  • Percentile Rank = (5 + 0.5 * 1) / 8 * 100
  • 5 + 0.5 = 5.5
  • 5.5 / 8 = 0.69
  • 0.69 * 100 = 69
• Interpretation: The student who scored 18 performed better than 69% of the class.

Conclusion

• Discussed the meaning and calculation process of percentile rank.
• This methodology can be used in various types of data analysis.

Closing

• Hope this discussion was helpful.
• Stay safe and healthy always.
• See you in the next video.