Consider the set of values below. At what percentile is 32 1 1 2 3 5 8 13 21 32 56 88 88 88 88 88 32 is at the th percentile ( Simplify your answer)
To find the percentile of 32, we first need to determine its rank. The rank of a value represents the position it holds in the ordered set of values.
The given set of values is already ordered from smallest to largest:
1 1 2 3 5 8 13 21 32 56 88 88 88 88 88
The rank of 32 can be found by counting the number of values that are smaller than it, and adding 1 (to account for the value itself):
Rank of 32 = (number of values smaller than 32) + 1 = 9 + 1 = 10
To find the percentile corresponding to this rank, we can use the formula:
percentile = (rank / total number of values) x 100
In this case, there are 16 values in the set, so the total number of values is 16. Therefore:
percentile = (10 / 16) x 100 ≈ 62.5
So 32 is at the 62.5th percentile.
To find the percentile at which the value 32 is located, we need to determine the relative position of 32 among the given values.
First, we arrange the values in ascending order: 1 1 2 3 5 8 13 21 32 32 56 88 88 88 88 88.
There are a total of 16 values in the set. To find the percentile, we need to determine the rank of 32.
The formula to calculate rank percentile is given by:
Rank = (P / 100) * (N + 1)
where P is the percentile and N is the total number of values.
Let's calculate the rank for 32:
Rank = (P / 100) * (16 + 1)
Rank = (P / 100) * 17
To simplify the answer, we need to find a value for P that satisfies the equation:
32 = (P / 100) * 17
To find P, we can rearrange the equation as follows:
P = (32 * 100) / 17
P = 188.24
Therefore, 32 is approximately at the 188th percentile.