To determine how many students scored higher than the 80th percentile, we can follow these steps:

1. Sort the scores (they are already sorted in ascending order):
   45.8, 57, 59.2, 64.4, 66.4, 67, 73.4, 75, 75.8, 80.5, 81.5, 86.3, 90.8, 91.4, 97.8

2. Find the 80th percentile: Since there are 15 students, the 80th percentile score corresponds to the score of the student ranked in the $0.80 \times 15 = 12^{\text{th}}$ position in the sorted list (rounded up).

   The 12th score in the sorted list is 86.3.

3. Count the students who scored higher than 86.3: The scores higher than 86.3 are:

   • 90.8, 91.4, 97.8

   So, 3 students scored higher than the 80th percentile.

4. Calculate the percentage of students who scored higher than the 80th percentile: $\frac{3}{15} \times 100 = 20\%$

Thus, there were 3 students that scored higher than the 80th percentile, which is 20% of the students.

Would you like more details or have any questions?

Related questions:

1. How do you calculate percentile rank in general?
2. How is the 80th percentile different from the median or the mean score?
3. What does scoring above the 80th percentile indicate in terms of performance?
4. How do you handle percentile calculations with larger datasets?
5. How does the percentile formula change if the total number of students changes?

Tip:

When calculating percentiles in a small dataset, it's important to be careful with rounding and ensure the correct placement within the ordered list.