Find the values of the 30th and 90th percentiles of the data. Please show your work.
129, 113, 200, 100, 105, 132, 100, 176, 146, 152
A percentile is a measure used indicating the value below which a given percentage of observations in a group of observations fall.
Arrange in order of value, lowest to highest. Third value = 30th percentile.
To find the values of the 30th and 90th percentiles of the data, we will follow these steps:
1. Sort the data in ascending order:
100, 100, 105, 113, 129, 132, 146, 152, 176, 200.
2. Calculate the index position for the 30th percentile:
Index = (30/100) * (N + 1) = (30/100) * (10 + 1) = 3.3.
Since the index is not a whole number, we will round it up to the next integer.
Thus, the index position for the 30th percentile is 4.
3. Find the value at the 30th percentile:
The value at the 30th percentile will be the number at the index position 4.
In this case, the 30th percentile value is 113.
4. Calculate the index position for the 90th percentile:
Index = (90/100) * (N + 1) = (90/100) * (10 + 1) = 9.9.
Since the index is not a whole number, we will round it up to the next integer.
Thus, the index position for the 90th percentile is 10.
5. Find the value at the 90th percentile:
The value at the 90th percentile will be the number at the index position 10.
In this case, the 90th percentile value is 200.
Therefore, the values of the 30th and 90th percentiles of the data are 113 and 200, respectively.