Final answer:
To tell which data set has the greatest standard deviation, compare how data values are spread from the mean; a larger standard deviation indicates more spread out values. Graphs such as histograms and box plots help visualize the data spread, while calculators or software provide accurate calculations. Data sets with higher standard deviations demonstrate greater variability.
Step-by-step explanation:
To determine which data set has the greatest standard deviation, you need to consider how the data values are spread around the mean. A data set with a large standard deviation has values that are more widely spread out from the mean, indicating higher variability. Conversely, a smaller standard deviation suggests that data values are closer to the mean, with less variability.
When comparing standard deviations, you can visualize the spread by graphing the data in histograms or box plots. Such visuals can help contrast symmetrical distributions, where the standard deviation is more homogeneous, with skewed distributions, where the disparity can render the standard deviation less informative. In skewed distributions, it is recommended to examine the median and quartiles for a better understanding of the spread.
It's important to use a calculator or computer software to calculate the standard deviation accurately. For instance, if you are using a TI-83, 83+, or 84+ calculator, you would select the summary statistics option and choose either 'ox' or 'sx' for sample or population standard deviation, respectively.
Supermarket B, with its higher standard deviation compared to Supermarket A, demonstrates greater variability in wait times. Thus, the standard deviation can indeed be used to assess whether a data value is close to or far from the mean, offering insights into the overall variation within the data set.