To find the 75th percentile, we first need to arrange the data in ascending order and then calculate the position of the percentile in the ordered list.
First, let’s sort the data:
- 16
- 25
- 28
- 32
- 35
- 38
- 42
Now, we have the sorted data: 16, 25, 28, 32, 35, 38, 42.
Next, we calculate the position of the 75th percentile using the formula:
P = (n + 1) * (percentile / 100), where n is the number of data points.
Here, n = 7 (since we have 7 data points). So, we calculate:
P = (7 + 1) * (75 / 100) = 8 * 0.75 = 6
The position is 6, which means the 75th percentile corresponds to the 6th value in the sorted list.
Looking at our sorted data:
- 1st: 16
- 2nd: 25
- 3rd: 28
- 4th: 32
- 5th: 35
- 6th: 38
- 7th: 42
Thus, the 75th percentile score is 38.