To compute percentiles for the given data set, you'll first need to arrange the data in ascending order, and then you can use the following formulas:
1. **20th Percentile (P20)**: This is the value below which 20% of the data falls.
2. **25th Percentile (P25)**: This is the value below which 25% of the data falls.
3. **65th Percentile (P65)**: This is the value below which 65% of the data falls.
4. **75th Percentile (P75)**: This is the value below which 75% of the data falls.
Let's calculate these percentiles for the given data set:
Arranging the data in ascending order: 15, 20, 25, 25, 27, 28, 30, 34
1. **20th Percentile (P20)**:
- 20% of the data is (20/100) * 8 = 1.6 (round up to 2 since it's the 2nd data point)
- The 2nd data point is 20.
- So, P20 = 20
2. **25th Percentile (P25)**:
- 25% of the data is (25/100) * 8 = 2
- The 2nd and 3rd data points are both 25.
- So, P25 = (25 + 25) / 2 = 25
3. **65th Percentile (P65)**:
- 65% of the data is (65/100) * 8 = 5.2 (round up to 6)
- The 6th data point is 28.
- So, P65 = 28
4. **75th Percentile (P75)**:
- 75% of the data is (75/100) * 8 = 6
- The 6th and 7th data points are 28 and 30.
- So, P75 = (28 + 30) / 2 = 29
So, the percentiles for the given data set are:
- 20th Percentile (P20) = 20
- 25th Percentile (P25) = 25
- 65th Percentile (P65) = 28
- 75th Percentile (P75) = 29