The formula for finding the rank of observations corresponding to a specific quartile or percentile is defined as which of the following?

The formula for finding the rank of observations corresponding to a specific quartile or percentile is often expressed as k = (p)(n) + p, where 'k' represents the rank or position of the observation, 'p' is the percentile expressed as a decimal (for example, 25% as 0.25), and 'n' is the total number of observations.

This formula accounts for the rank by calculating the cumulative position based on the total number of observations and the desired percentile. After calculating (p)(n), which gives an initial rank based on the proportion of data falling below that percentile, the addition of 'p' helps adjust for the exact position in cases where the data set might not be perfectly divisible. This ensures that the rank aligns correctly with the observation in the ordered dataset.

The other formulas do not correctly reflect the method for determining the rank for percentiles or quartiles as they either don't incorporate the necessary adjustments or misrepresent how to calculate the rank within a dataset. Hence, the selection of k = (p)(n) + p is accurate for determining the correct position corresponding to the specified percentile.