Question

raquel and van live in two different cities. as part of a project, they each record the lowest prices for a gallon of gas at gas stations around their cities on the same day. raquels data show $\bar{x}=3.42$ and $sigma=0.07$. vans data show $\bar{x}=3.78$ and $sigma=0.23$.
which statement is true about their gas-price data?
○ raquels data are most likely closer to $3.42 than vans data are to $3.78.
○ vans data are most likely closer to $3.42 than raquels data are to $3.78.
○ raquels data are most likely closer to $3.78 than vans data are to $3.42.
○ vans data are most likely closer to $3.78 than raquels data are to $3.42.

Explanation:

Step1: Understand standard deviation meaning

Standard deviation ($\sigma$) measures data spread around the mean ($\bar{x}$). A smaller $\sigma$ means data is closer to its mean.

Step2: Compare the two datasets

Raquel: $\bar{x}=3.42$, $\sigma=0.07$ (small spread, data close to 3.42)
Van: $\bar{x}=3.78$, $\sigma=0.23$ (large spread, data farther from 3.78)
This means Raquel's data is closer to its mean ($3.42$) than Van's data is to its mean ($3.78$).

Answer:

Raquel's data are most likely closer to $3.42 than Van's data are to $3.78.