Let's analyze the statements provided regarding Raquel's and Van's gas-price data.
1. Given Data:
- Raquel's average gas price ([tex]\(\bar{x}_R\)[/tex]) is \[tex]$3.42 with a standard deviation (\(\sigma_R\)) of 0.07.
- Van's average gas price (\(\bar{x}_V\)) is \$[/tex]3.78 with a standard deviation ([tex]\(\sigma_V\)[/tex]) of 0.23.
2. Understanding the Mean ([tex]\(\bar{x}\)[/tex]) and Standard Deviation ([tex]\(\sigma\)[/tex]):
- The mean is the average value of all gas prices recorded.
- The standard deviation indicates how much the gas prices vary from the mean. A smaller standard deviation signifies that the data points are closer to the mean, whereas a larger standard deviation signifies more variability in the data points around the mean.
3. Comparison of Standard Deviations:
- Raquel's data have a standard deviation of 0.07, which is quite small.
- Van's data have a standard deviation of 0.23, which is larger compared to Raquel's.
4. Interpreting the Standard Deviation in Context:
- Since Raquel's standard deviation (0.07) is smaller than Van's (0.23), Raquel's gas prices are more tightly clustered around her mean price of \[tex]$3.42.
- On the other hand, Van's higher standard deviation means his gas prices are more spread out around his mean price of \$[/tex]3.78.
5. Conclusion:
- Given that Raquel has a smaller standard deviation, it means her recorded gas prices are more consistently close to the mean value of \[tex]$3.42.
- Therefore, we can conclude that Raquel's data are most likely closer to \$[/tex]3.42 than Van's data are to \[tex]$3.78.
Hence, the correct statement is:
Raquel's data are most likely closer to \$[/tex]3.42 than Van's data are to \[tex]$3.78.
So, the true statement is:
Raquel's data are most likely closer to \$[/tex]3.42 than Van's data are to \$3.78.
