Question at position 40 Here is a list of exam scores for Mr. William's calculus class: 60 61 61 65 72 75 75 78 81 85 89 91 98 What is the percentile corresponding to the person whose score was 85?33rd50th75th77th73rd

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BlackTom AI · Accepted Answer

First, let's restate the data and the question in my own words to ensure clarity. We have an ordered list of 13 exam scores: 60, 61, 61, 65, 72, 75, 75, 78, 81, 85, 89, 91, 98. We are asked to find the percentile corresponding to the score of 85.
Option 1: 33rd. This would imply that roughly one-third of the scores are at or below 85. In this data set, there are 10 scores at or below 85, which already gives a percentile well above 33rd. So 33rd is clearly too low.
Option 2: 50th. The 50th percentile (the median) in a 13-item list would correspond to the 7th value when using a standard median position (i = 7). The 7th value is 75, not 85, and the percentile for 85 would be higher than the median. Hence 50th is not correct.
Option 3: 75th. If we used a simple method where percentile equals (rank of the value)/N, with the 10th value (85) giving 10/13 ≈ 76.9th percentile, that would round to about 77th, not 75th. Some teaching materials round differently, but the commonly accepted direct rank method would not produce exactly 75th for the 10th value here. Also, that method would be too low relative to the actual position of 85 in the ordered data. So 75th is unlikely.
Option 4: 77th. As just discussed, using the straightforward rank method (including 85 as the 10th item) would yield around 76.9 or 77 when rounded. This option is plausible if we used the simple (i/N)*100 approach, but we need to check the precise percentile calculation rule being intended.
Option 5: 73rd. This matches a common percentile calculation that uses the formula percentile = ((i − 0.5) / N) × 100, where i is the rank of the value in the ordered list. Here, the value 85 is at rank i = 10 (since it is the 10th item in the sorted list). Plugging in, percentile = ((10 − 0.5) / 13) × 100 = (9.5 / 13) × 100 ≈ 73.08, which rounds to 73rd. This aligns with the provided correct answer and with a standard approach that avoids over- or under-stating the percentile for discrete data.

In summary, considering the common percentile calculation that uses (i − 0.5)/N to place a value within the distribution, the score 85 corresponds to about 73rd percentile. The other options misestimate because they rely on different thresholds or rounding rules that either underestimate (33rd, 50th, 75th) or overstate (77th) the position, given the rank of 85 is 10th in the ordered list. The key idea is recognizing the rank of 85 and applying the (i − 0.5)/N rule to place it properly within the 13-item distribution.

Question at position 40 Here is a list of exam scores for Mr. William's calculus class: 60 61 61 65 72 75 75 78 81 85 89 91 98 What is the percentile corresponding to the person whose score was 85?33rd50th75th77th73rd

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