Ranking with Ties
Ranking with Ties problems involve scenarios where multiple persons achieve the same rank (tie). When ties occur, the next rank skips ahead (e.g., 1,2,2,4). These problems test your understanding of rank assignment with ties and the difference between rank position and count of persons.
What You'll Learn
Introduction to Ranking with Ties
Ranking with Ties problems involve scenarios where multiple persons achieve the same rank (tie). When ties occur, the next rank skips ahead (e.g., 1,2,2,4). These problems test your understanding of rank assignment with ties and the difference between rank position and count of persons.
Prerequisites
How to Solve Ranking with Ties Problems
Step 1: Identify all persons and their scores/values
Step 2: Group persons with equal scores (ties)
Step 3: Assign the same rank to all persons in a tied group
Step 4: Skip ranks equal to (number in tied group - 1) before next rank
Step 5: For rank of a person, count how many have higher scores, add 1
Step 6: For number of persons below a rank, count persons with lower scores
Step 7: Answer the specific question
Example Problem
Example: Scores: A=95, B=90, C=90, D=85, E=80. What are the ranks? Solution: Step 1: Sort descending: A(95), B(90), C(90), D(85), E(80) Step 2: Ties: B and C both 90 Step 3: Assign: A rank 1, B and C rank 2 (tie), D rank 4 (skip 3), E rank 5 Answer: A=1, B=2, C=2, D=4, E=5
Pro Tips & Tricks
- Rank = 1 + (number of persons with higher score)
- If k persons share rank r, next rank is r + k
- Total ranks = number of distinct score groups
- The sum of all ranks (using competition ranking) = not meaningful
- In 'dense ranking', ties don't skip numbers (1,2,2,3)
- In 'competition ranking', ties cause skips (1,2,2,4)
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Ranking with Ties. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Ranking with Ties is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Ranking with Ties?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: