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 = 0.23 ). 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 the concept of standard deviation

Standard deviation ($\sigma$) measures the spread of data. A smaller standard deviation means data points are closer to the mean ($\overline{x}$).
Raquel has $\sigma = 0.07$ and Van has $\sigma=0.23$. Since $0.07<0.23$.

Step2: Analyze the relationship between data and mean

Raquel's data, with a smaller standard deviation, is more clustered around its mean ($\overline{x}_{Raquel}=3.42$) than Van's data is around its mean ($\overline{x}_{Van} = 3.78$).

Answer:

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