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 of each student

Clarissa's standard deviation is 12.53, Abi's is 8.99, Kaila's is 15.29, and Shenika's is 7.67.

Step3: Analyze each option

• Option 1: Shenika's std. dev. (7.67) < Clarissa's std. dev. (12.53), so Shenika's monthly salary is less spread out than Clarissa's.
• Option 2: Kaila's std. dev. (15.29) > Abi's std. dev. (8.99), so Kaila's salary is more spread out than Abi's.
• Option 3: Abi's std. dev. (8.99) > Shenika's std. dev. (7.67), so Abi's salary is more spread out than Shenika's.
• Option 4: Clarissa's std. dev. (12.53) > Abi's std. dev. (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.