The monthly mean salaries and standard deviations of four college students are given below.

\begin{tabular}{|c|c|c|}
\hline
Student & Mean & Standard Deviation \\
\hline
Clarissa & \[tex]$345 & 12.53 \\
\hline
Abi & \$[/tex]598 & 8.99 \\
\hline
Kaila & \[tex]$812 & 15.29 \\
\hline
Shenika & \$[/tex]208 & 7.67 \\
\hline
\end{tabular}

Which statement must be true?

A. The monthly salary of Shenika is less spread out than the monthly salary of Clarissa.
B. The monthly salary of Kaila is less spread out than the monthly salary of Abi.
C. The monthly salary of Abi is less spread out than the monthly salary of Shenika.
D. The monthly salary of Clarissa is less spread out than the monthly salary of Abi.



Answer :

To determine which statements are true regarding the spread of the monthly salaries of the students, we need to compare their standard deviations. The standard deviation is a measure of the amount of variation or dispersion in a set of values.

Given the standard deviations:
- Clarissa: 12.53
- Abi: 8.99
- Kaila: 15.29
- Shenika: 7.67

Let's evaluate each statement step by step:

1. The monthly salary of Shenika is less spread out than the monthly salary of Clarissa.
- Shenika's standard deviation: 7.67
- Clarissa's standard deviation: 12.53
- Since 7.67 < 12.53, Shenika's salary is indeed less spread out than Clarissa's.

2. The monthly salary of Kaila is less spread out than the monthly salary of Abi.
- Kaila's standard deviation: 15.29
- Abi's standard deviation: 8.99
- Since 15.29 > 8.99, Kaila's salary is not less spread out than Abi's.

3. The monthly salary of Abi is less spread out than the monthly salary of Shenika.
- Abi's standard deviation: 8.99
- Shenika's standard deviation: 7.67
- Since 8.99 > 7.67, Abi's salary is not less spread out than Shenika's.

4. The monthly salary of Clarissa is less spread out than the monthly salary of Abi.
- Clarissa's standard deviation: 12.53
- Abi's standard deviation: 8.99
- Since 12.53 > 8.99, Clarissa's salary is not less spread out than Abi's.

Therefore, based on the comparisons of their standard deviations, the statement that must be true is:

The monthly salary of Shenika is less spread out than the monthly salary of Clarissa.