Question

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

student	mean	standard deviation
abi	$598	8.99
kaila	$812	15.29
shenika	$208	7.67

which statement must be true?

• the monthly salary of clarissa is less spread out than the monthly salary of abi.
• the monthly salary of shenika is less spread out than the monthly salary of clarissa.
• the monthly salary of kaila is less spread out than the monthly salary of abi.
• the monthly salary of abi is less spread out than the monthly salary of shenika.

Explanation:

Step1: Recall standard deviation meaning

Standard deviation measures data spread. Lower value means less spread.

Step2: Compare Clarissa and Abi

Clarissa's SD: $12.53$, Abi's SD: $8.99$. $12.53 > 8.99$, so Clarissa's is more spread. First statement false.

Step3: Compare Shenika and Clarissa

Shenika's SD: $7.67$, Clarissa's SD: $12.53$. $7.67 < 12.53$, so Shenika's is less spread. Second statement true.

Step4: Compare Kaila and Abi

Kaila's SD: $15.29$, Abi's SD: $8.99$. $15.29 > 8.99$, so Kaila's is more spread. Third statement false.

Step5: Compare Abi and Shenika

Abi's SD: $8.99$, Shenika's SD: $7.67$. $8.99 > 7.67$, so Abi's is more spread. Fourth statement false.

Answer:

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