How is a percentile calculated?

The calculation of a percentile involves determining the position of a specific value within a data set by ranking the values in ascending order. The formula for calculating a percentile is designed to show how a particular value compares to the rest of the values in the dataset.

When you use the formula (number of values below x / total number of values) × 100, you are effectively measuring the percentage of data points that fall below the specified value x. This results in a percentile ranking that indicates where x stands in relation to the rest of the data. For example, if x is at the 75th percentile, this means that 75% of the data points are below x, which provides a clear understanding of the distribution of the data.

The other methods listed do not accurately represent how percentiles are calculated. For instance, dividing the total number of values by the rank of x does not provide the percentage of values below x and thus does not convey the requisite information about the data distribution. Averaging the values gives a mean but does not relate to the individual ranking or position of a specific value. Identifying maximum and minimum values addresses the range of the data but does not involve percentiles or their calculation. Therefore, the first choice accurately describes how