In a dataset, what does it mean to say that a value is at the 83rd percentile?

• A. The value is exactly 83% of the maximum observation in the dataset.
• B. About 83% of the observations are less than or equal to that value.
• C. About 83% of the observations are greater than or equal to that value.
• D. The value is the same as the third quartile ($Q_3$).

Answer: (B)

Verified step by step guidance

1. Understand that a percentile indicates the relative standing of a value within a dataset, showing the percentage of data points below or equal to that value.
2. Recognize that the 83rd percentile means that approximately 83% of the observations in the dataset are less than or equal to the value at this percentile.
3. Note that this does not mean the value is 83% of the maximum observation; percentiles relate to the position in the ordered data, not the magnitude relative to the maximum.
4. Understand that the 83rd percentile is not the same as the third quartile (Q\_3), which corresponds to the 75th percentile, so these are different concepts.
5. Conclude that the correct interpretation of a value at the 83rd percentile is: about 83% of the observations are less than or equal to that value.