Final answer:
The statistic describing dispersion around the mean in quality control is the standard deviation, indicating how spread out data values are from the mean.
Step-by-step explanation:
When determining quality control, the statistic that describes dispersion around the mean is the standard deviation. This measure of variability indicates how spread out the data values are from the mean. If the standard deviation is zero, this means all data values are the same; as the standard deviation increases, the data values are more dispersed around the mean, showing greater variability.
The standard error of the mean is another related concept, representing the standard deviation of the sampling distribution and reflecting the average standard deviation from repeated sampling of a population. Chebyshev's Rule and the Empirical Rule use standard deviation to describe the spread of data in different types of distributions, with the Empirical Rule applying specifically to bell-shaped, symmetric distributions.