Final answer:
To determine the specific percentiles of commute distances to a college, order the data and use the positions P20, Q1, and Q3 by multiplying the total number of data points by 0.20, 0.25, and 0.75 respectively.
Step-by-step explanation:
The question seeks to find the 20th percentile, 25th percentile (first quartile), and 75th percentile (third quartile) of a set of data representing students' commute distances to a college. To find the percentiles, you would arrange the data in ascending order and use the appropriate formulas or methods to locate the values that correspond to each specified percentile. For the 20th percentile, which is also known as P20, you would multiply the total number of data points by 0.20. Likewise, for the 25th and 75th percentiles (Q1 and Q3), you would use 0.25 and 0.75, respectively, then round up to the nearest whole number to find the position in the ordered data set. If the calculation results in a fractional position, you would interpolate between the two closest values.