the monthly mean salaries and standard deviations of four college students are given below.\n| student |…
the monthly mean salaries and standard deviations of four college students are given below.\n| student | mean | standard deviation |\n|--|--|--|\n| clarissa | $345 | 12.53 |\n| abi | $598 | 8.99 |\n| kaila | $812 | 15.29 |\n| shenika | $208 | 7.67 |\nwhich statement must be true?\nthe monthly salary of shenika is less spread out than the monthly salary of clarissa\nthe monthly salary of kaila is less spread out than the monthly salary of abi\nthe monthly salary of abi is less spread out than the monthly salary of shenika\nthe monthly salary of clarissa is less spread out than the monthly salary of abi
Answer
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