To find the 45th percentile of the number of nuclear reactors in the given countries, we first need to list the number of reactors in ascending order.
Here are the numbers of reactors listed in ascending order:
1 (Iran)
1 (Slovenia)
2 (Bulgaria)
2 (South Africa)
4 (Finland)
4 (Hungary)
4 (Slovakia)
5 (Switzerland)
6 (Czech Republic)
8 (Spain)
10 (Sweden)
18 (China)
19 (Canada)
20 (India)
33 (Russia)
15 (Ukraine)
16 (United Kingdom)
50 (Japan)
58 (France)
100 (United States)
Now let's organize the data in ascending order:
1, 1, 2, 2, 4, 4, 4, 5, 6, 8, 10, 15, 16, 18, 19, 20, 33, 50, 58, 100
Next, we need to find the rank for the 45th percentile. The formula for calculating the rank (position) of the percentile is:
\[ P = \frac{n \cdot k}{100} \]
where:
- \( P \) is the position
- \( n \) is the total number of observations
- \( k \) is the desired percentile (in this case, 45)
In this case, we have 20 countries (total number of observations), so:
\[ P = \frac{20 \cdot 45}{100} = 9 \]
The rank is 9. Because this is a whole number, the 45th percentile will be the average of the 9th and 10th values in our ordered list.
The 9th and 10th values from the ordered list are:
9th value: 6
10th value: 8
Now, we find the average of these two values:
\[ \text{Average} = \frac{6 + 8}{2} = \frac{14}{2} = 7 \]
Therefore, the 45th percentile of the number of nuclear reactors is 7.
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