Question

Find the percentile rank for each value in the data set. The data represent the values in billions of dollars of the damage of 10 hurricanes: 1.1, 1.7, 1.9, 2.1, 2.2, 2.5, 3.3, 6.2, 6.8, 20.3.

Answer 1

The value at position 5 in the ordered data set is the 40th percentile. The data set is [1.1, 1.7, 1.9, 2.1, 2.2, 2.5, 3.3, 6.2, 6.8, 20.3], so the value at position 5 is 2.2 billion dollars.

To find the percentile rank for each value in the data set, we first need to order the data from smallest to largest, which has already been done. The percentile rank for a given value is the percentage of data that falls below that value.

The formula for the percentile rank P of a given value is:

`\[ P = \left( \frac{\text{Number of values below the given value} + 0.5}{\text{Total number of values}} \right) * 100 \]`

The given data set already appears to be in ascending order. There are 10 values in total.

To find the 40th percentile, we use the following steps:

1. Calculate the index:
`\( i = P * (N+1)/(100) \)`, where
`\( P \)` is the desired percentile (in this case, 40) and N is the total number of observations (in this case, 10).

2. If i is not an integer, round up to the nearest whole number, and that position in the ordered list is the value for the 40th percentile.

3. If i is an integer, the 40th percentile is the average of the values at positions i and i+1 in the ordered list.

Let's calculate the index for the 40th percentile and then determine the corresponding value from the data set.

The value corresponding to the 40th percentile in the data set is 2.2 billion dollars.

Detailed Calculation Steps:

1. Calculate the Index:

`\[ i = (40)/(100) * (10 + 1) = 4.4 \]`

2. Determine the Position:

Since the index
`\( i \)` is not an integer, we round up to the nearest whole number to get the position in the ordered list. Rounding up 4.4 gives us position 5 (since we start counting from 1 in the list).

3. Find the 40th Percentile Value:

The value at position 5 in the ordered data set is the 40th percentile. The data set is [1.1, 1.7, 1.9, 2.1, 2.2, 2.5, 3.3, 6.2, 6.8, 20.3], so the value at position 5 is 2.2 billion dollars.

the complete Question is given below:

Hurricane Damage. Find the Percentile rank for each value in the data set. The data represent the values in billions of the damage of 10 hurricanes. 1.1, 1.7, 1.9, 2.1, 2.2, 2.5, 3.3, 6.2, 6.8, 20.3. what value corresponds to the 40th Percentile?