Question

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

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 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
the monthly salary of clarissa is less spread out than the monthly salary of abi

Explanation:

Step1: Recall the meaning of standard - deviation

Standard deviation measures the spread of data. A lower standard deviation means the data is less spread out.

Step2: Compare the standard deviations

We have standard deviations: Clarissa ($12.53$), Abi ($8.99$), Kaila ($15.29$), Shenika ($7.67$).

• For Shenika ($7.67$) and Clarissa ($12.53$), since $7.67<12.53$, Shenika's monthly salary is less spread out than Clarissa's.
• For Kaila ($15.29$) and Abi ($8.99$), $15.29 > 8.99$, so Kaila's salary is more spread out than Abi's.
• For Abi ($8.99$) and Shenika ($7.67$), $8.99>7.67$, so Abi's salary is more spread out than Shenika's.
• For Clarissa ($12.53$) and Abi ($8.99$), $12.53>8.99$, so Clarissa's salary is more spread out than Abi's.

Answer:

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