Let's examine the given statements and determine which one must be true based on the provided standard deviations:
1. The monthly salary of Shenika is less spread out than the monthly salary of Clarissa.
- Shenika's standard deviation: [tex]\(7.67\)[/tex]
- Clarissa's standard deviation: [tex]\(12.53\)[/tex]
We compare [tex]\(7.67 < 12.53\)[/tex]:
- This statement is TRUE.
2. The monthly salary of Kaila is less spread out than the monthly salary of Abi.
- Kaila's standard deviation: [tex]\(15.29 \)[/tex]
- Abi's standard deviation: [tex]\(8.99 \)[/tex]
We compare [tex]\(15.29 < 8.99\)[/tex]:
- This statement is FALSE.
3. The monthly salary of Abi is less spread out than the monthly salary of Shenika.
- Abi's standard deviation: [tex]\(8.99\)[/tex]
- Shenika's standard deviation: [tex]\(7.67\)[/tex]
We compare [tex]\(8.99 < 7.67\)[/tex]:
- This statement is FALSE.
4. The monthly salary of Clarissa is less spread out than the monthly salary of Abi.
- Clarissa's standard deviation: [tex]\(12.53\)[/tex]
- Abi's standard deviation: [tex]\(8.99\)[/tex]
We compare [tex]\(12.53 < 8.99\)[/tex]:
- This statement is FALSE.
From the above analysis:
- Statement 1 is true.
- Statements 2, 3, and 4 are false.
Therefore, the statement that must be true is the first one:
"The monthly salary of Shenika is less spread out than the monthly salary of Clarissa."
