Percentage and percentile are both measures used in statistics and data analysis, but they serve different purposes and provide different types of information. Here is the key difference between Percentage and Percentile:

__1. Definition__

**Percentage**

- A way to express a number as a fraction of 100.
- Indicates a proportion out of 100.
- Calculated by dividing the part by the whole and multiplying by 100.

**Percentile**

- A measure that indicates the relative standing of a value within a data set.
- Represents the value below which a given percentage of observations in a group of observations fall.
- For example, the 50th percentile (median) is the value below which 50% of the data falls.

__2. Calculation__

**Percentage**

- Formula: \ ((\text {Part} / \text {Whole}) \times 100\).
- Example: If 45 out of 60 questions are answered correctly, the percentage is \ ((45 / 60) \times 100 = 75\%\).

**Percentile**

- Determined by ranking the data set in ascending order and finding the value below which a certain percentage of data falls.
- Example: In a data set of test scores, if a score of 85 is in the 90th percentile, it means that 90% of the scores are below 85.

__3. Usage__

**Percentage**

- Used to compare proportions and ratios.
- Commonly used in everyday situations, such as calculating discounts, interest rates, and statistics in reports.

**Percentile**

- Used to understand the relative standing of a value within a data set.
- Commonly used in standardized testing, health metrics (e.g., growth charts for children), and other areas where relative performance is important.

__4. Interpretation__

**Percentage**

- Directly interpretable as a fraction of 100.
- Example: A score of 80% means 80 out of every 100.

**Percentile**

- Indicates the position of a value within a distribution.
- Example: Being in the 80th percentile means you scored better than 80% of the people.

__5. Examples__

**Percentage**

- A student scores 75 out of 100 on a test, which is 75%.
- A store offers a 20% discount on all items.

**Percentile**

- A child's weight is in the 60th percentile, meaning 60% of children weigh less than that child.
- In a group of 100 runners, if you finish in the 10th percentile, you are faster than 90 runners.

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