Which of the following statements is most accurate when defining $percentiles$ in probability and statistics?

• A. A $percentile$ is the average of all values in a dataset.
• B. A $percentile$ is the most frequently occurring value in a dataset.
• C. A $percentile$ is the difference between the maximum and minimum values in a dataset.
• D. A $percentile$ is the value below which a given percentage of observations in a dataset falls.

Answer: (D)

Verified step by step guidance

1. Understand that a percentile is a measure used in statistics to indicate the relative standing of a value within a dataset.
2. Recall that the average (mean) is the sum of all values divided by the number of values, which is different from a percentile.
3. Recognize that the most frequently occurring value is called the mode, not a percentile.
4. Know that the difference between the maximum and minimum values is called the range, which is also different from a percentile.
5. Conclude that a percentile is defined as the value below which a certain percentage of observations in the dataset fall, making this the most accurate statement.