The following table presents the number of nuclear reactors as of August, in some countries that had one or more reactors

Question

2
1
7
2
2
19
18
6
4
58
9
4
20
1
50
23
2
1
3
2
33
4

what is the 45th percentile?

Answer 1

To find the 45th percentile of a data set, you'll want to follow these steps:

1. Organize the Data: First, we need to sort the data in ascending order.

Given the values:

• 2, 1, 7, 2, 2, 19, 18, 6, 4, 58, 9, 4, 20, 1, 50, 23, 2, 1, 3, 2, 33, 4

Organizing these in order:

• 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 6, 7, 9, 18, 19, 20, 23, 33, 50, 58

2. Calculate the Position: Next, we find the position of the 45th percentile using the formula:

   \[ P = \frac{n \cdot k}{100} \]

   Where \( n \) is the total number of data points, and \( k \) is the percentile (in this case, 45).

   We have 24 data points.

   \[ P = \frac{24 \cdot 45}{100} = 10.8 \]

   Since we're looking for a percentile and the result is not a whole number, we will round up to the next whole number. Thus, the position we are interested in is the 11th value when the data is sorted.

3. Find the 11th Value: Looking at our sorted list:

• Sorted List: 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 6, 7, 9, 18, 19, 20, 23, 33, 50, 58

The 11th value in the sorted list is 4.

Therefore, the 45th percentile of the number of nuclear reactors in this data set is 4.

Answer 2

what is the 88th percentile?

Answer 3

To find the 88th percentile of the data set, we will follow the same procedure we used for the 45th percentile:

1. Organize the Data: The sorted data set is:

   • Sorted List: 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 6, 7, 9, 18, 19, 20, 23, 33, 50, 58

2. Calculate the Position: The position of the 88th percentile can be calculated using the formula:

   \[ P = \frac{n \cdot k}{100} \]

   where \( n \) is the total number of data points (24), and \( k \) is 88.

   \[ P = \frac{24 \cdot 88}{100} = 21.12 \]

   Since \( 21.12 \) is not a whole number, we round it up to 22. This means we will find the value at the 22nd position in the sorted list.

3. Find the 22nd Value: Looking at our sorted list:

• Sorted List: 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 6, 7, 9, 18, 19, 20, 23, 33, 50, 58

The 22nd value in the sorted list is 33.

Therefore, the 88th percentile of the number of nuclear reactors in this data set is 33.