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 $overline{x}=3.42$ and $sigma = 0.07$. vans data show $overline{x}=3.78$ and $sigma = 0.21$.
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 the concept of standard deviation

Standard deviation ($\sigma$) measures the spread of data. A smaller standard deviation means data is more clustered around the mean. Raquel has $\sigma = 0.07$ (smaller) and mean $\bar{x}=3.42$. Van has $\sigma = 0.21$ (larger) and mean $\bar{x}=3.78$.

Step2: Analyze closeness

Since Raquel's data has a smaller standard deviation, her data points are more likely to be closer to her mean ($3.42$) compared to Van's data points being close to his mean ($3.78$) (because Van's data is more spread out due to larger $\sigma$).

Answer:

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