Question

Shannon is traveling from New York City to Washington, D.C. She wants to go by train so she can see the views. Since she will be driving home with a family member, she on priced the cost of a one-way ticket on Amtrak for any time of day on February 15. Below is an ordered listing of all fares that were available for selection on that day.

49 88 88 88 119 133 133 133 161 171 173 173 173 272 284
49 88 88 88 119 133 133 161 161 173 173 173 173 272 284
88 88 88 119 119 133 133 161 161 173 173 173 272 272 284
88 88 88 119 133 133 133 161 171 173 173 173 272 272 284
88 88 88 119 133 133 133 161 171 173 173 173 272 284 284
88 88 88 119 133 133 133 161 171 173 173 173 272 284 284

a. Find the percentile rank for a fare of $119.

Answer 1

To calculate the percentile rank for the fare of $119, the fares must be listed in ascending order to count those that are less or equal to $119. We then apply the percentile rank formula using the count obtained.

Step-by-step explanation:

To find the percentile rank for a fare of $119, we must first arrange all of the fares in ascending order, then count how many fares are less than or equal to $119. By listing the fares, we can see exactly how many times the fare of $119 appears and find its position relative to the rest of the fares.

With the fares arranged, we count the number of fares below $119 and then use the following percentile rank formula: Percentile Rank = (Number of values below X + 0.5) / Total number of values × 100%, where X is the value we are finding the percentile for, which in this case is $119. After counting the number of fares that are less than or equal to $119, we then plug the values into the formula to get the percentile rank.