To determine which option represents a strong "NO RELATION," we need to find the position of 'X' that is closest to zero. This is because a value of zero indicates no correlation or no relation in statistical contexts.
Let's examine each of the given options step-by-step:
1. [tex]$-1--0---X+1$[/tex]
- In this option, 'X' is positioned closest to zero, which is approximately -0.5.
2. [tex]$-1---X---+1$[/tex]
- Here, 'X' is farther from zero compared to option 1 and approximately corresponds to -1.
3. [tex]$-1---0--X-+1$[/tex]
- In this option, 'X' is positioned slightly to the right of zero, which is approximately +0.5.
4. [tex]$-1 X---0---+1$[/tex]
- Here, 'X' is positioned closest to -1, which is also quite far from zero.
After analyzing the positions of 'X':
- Option 1 has 'X' close to -0.5
- Option 2 has 'X' close to -1
- Option 3 has 'X' close to +0.5
- Option 4 has 'X' close to -1
The distance from zero (no relation) for each option is:
1. ~0.5 (closer to zero)
2. 1
3. ~0.5 (closer to zero)
4. 1
Comparing these distances, option 1 (with a position of approximately -0.5) is closest to zero, indicating the least amount of relationship, and therefore represents a strong "NO RELATION."
Thus, the option that represents a strong "NO RELATION" is:
Option 1.
