To determine which statement is true about their gas-price data, we need to analyze the given means and standard deviations for both Raquel and Van.
1. Raquel's Data:
- Mean ([tex]\(\bar{x}\)[/tex]): \[tex]$3.42
- Standard Deviation (\(\sigma\)): 0.07
2. Van's Data:
- Mean (\(\bar{x}\)): \$[/tex]3.78
- Standard Deviation ([tex]\(\sigma\)[/tex]): 0.23
The standard deviation measures the amount of variation or dispersion in a set of values. A smaller standard deviation indicates that the values tend to be closer to the mean of the set, while a larger standard deviation indicates that the values are spread out over a wider range.
- Raquel's standard deviation is 0.07, which is smaller than Van's standard deviation of 0.23. This means that Raquel's gas prices are more tightly clustered around her mean value of \[tex]$3.42.
- Van's standard deviation is 0.23. This larger value indicates that Van's gas prices are more spread out around his mean value of \$[/tex]3.78.
Given that Raquel's standard deviation is smaller than Van's, Raquel's data points are more likely to be closer to her mean of \[tex]$3.42 compared to how close Van's data points are to his mean of \$[/tex]3.78.
Therefore, the correct statement is:
- Raquel's data are most likely closer to \[tex]$3.42 than Van's data are to \$[/tex]3.78.
