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Based on the picture, why is there 4th, 12th and 14th rank in the ranking of scores?

The picture demonstrates how to rank scores when multiple students share the same score. The concept explained is **rank averaging**, which is applied to identical scores to avoid unfairness.

For example:
- **Rank 4th** exists because the score 48 is unique. Therefore, it gets the rank 4th.
- **Rank 12th and 14th** appear because the score 39 occurs three times. When multiple students have the same score, their ranks are averaged:
  - The students who scored 39 would normally get the ranks 12th, 13th, and 14th.
  - The sum of these ranks is \(12 + 13 + 14 = 39\).
  - Dividing by the number of students (3), each student is assigned the **average rank** of \( \frac{39}{3} = 13th \).
  
This process ensures that all students sharing the same score receive the same rank. That's why you see ranks like 12th, 13th, and 14th being used in this way.

Would you like more details or have any questions?

Here are five questions that can help deepen understanding:
1. How does rank averaging work when more than three scores are the same?
2. Why is it important to average ranks for identical scores?
3. How would the ranking change if no scores were identical?
4. Can the same method be applied if scores were decimal values instead of whole numbers?
5. How does this ranking method impact the interpretation of test results?

**Tip:** Rank averaging ensures fairness when there are tied scores, as it distributes the available ranks equally among students sharing the same score.

This problem explains rank averaging when multiple students have the same score. It details how to calculate the average rank for tied scores using examples such as why there is a 12th, 13th, and 14th rank in a set of tied scores. Suitable for students in Grades 8-10.

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