Question at position 14 Here are the exam scores for the 15 students in Mrs. Stevenson’s statistics class:72 75 75 78 81 81 85 89 90 90 90 91 95 95 98Spencer is at the 80th percentile of the distribution. What score did Spencer earn on the exam?7578958191

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BlackTom AI · Accepted Answer

To determine Spencer's score at the 80th percentile, we first arrange the exam scores in increasing order: 72, 75, 75, 78, 81, 81, 85, 89, 90, 90, 90, 91, 95, 95, 98.
Next, we identify the position that corresponds to the 80th percentile. Different methods exist, but many classroom conventions use the position as the ceiling of 0.8 times the number of observations (n). With n = 15, 0.8 × 15 = 12.0, and the ceiling of that is 12. This means the 12th value in the ordered list is the 80th percentile.
The 12th value in the sorted list is 91, so the 80th percentile score is 91.
Now, evaluating the provided options:
- 75: This is one of the lower scores and clearly precedes the 80th percentile; it does not represent the cutoff for the top 20%.
- 78: Also a lower value well before the 12th position, not the 80th percentile.
- 95: While 95 appears among the higher scores, it is the 13th and 14th values; it corresponds to roughly the 87th–93rd percentile range, not the 80th exactly.
- 81: An intermediate score that sits around the middle of the distribution; it does not serve as the 80th percentile cutoff.
- 91: This is the 12th value in the ordered list, which matches the 80th percentile under this convention.
So, the correct choice is 91, since it represents the score at or just above the 80th percentile depending on the percentileDefinition used in this context.

Question at position 14 Here are the exam scores for the 15 students in Mrs. Stevenson’s statistics class:72 75 75 78 81 81 85 89 90 90 90 91 95 95 98Spencer is at the 80th percentile of the distribution. What score did Spencer earn on the exam?7578958191

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