Find the values of the 30th and 90th percentiles of the data
129, 113, 200, 100, 105, 132, 100, 176, 146, 152
Arrange in order of value from lowest to highest. 90th would be between 9th and 10th. 30th would be between 3rd and 4th.
To find the values of the 30th and 90th percentiles of the data, you can follow these steps:
1. Sort the data in ascending order: 100, 100, 105, 113, 129, 132, 146, 152, 176, 200.
2. Calculate the index values of the percentiles:
- For the 30th percentile: 30/100 * (n + 1) = 0.30 * (10 + 1) = 3.3. Since the index is not an integer, you need to interpolate between the values at indices 3 and 4.
- For the 90th percentile: 90/100 * (n + 1) = 0.90 * (10 + 1) = 9.9. Again, interpolate between the values at indices 9 and 10.
3. Find the values at the calculated indices:
- For the 30th percentile: Interpolate between the values at indices 3 and 4.
- Index 3: 105
- Index 4: 113
- Interpolated value: 105 + (0.3 * (113 - 105)) = 105 + 2.4 = 107.4
- For the 90th percentile: Interpolate between the values at indices 9 and 10.
- Index 9: 152
- Index 10: 176
- Interpolated value: 152 + (0.9 * (176 - 152)) = 152 + 21.6 = 173.6
So, the value of the 30th percentile is approximately 107.4, and the value of the 90th percentile is approximately 173.6.