Final answer:
The statement provided is true. Standard Deviation (σ) is a measure of how data values spread out around the mean and is critical for understanding the variability in a data set.
Step-by-step explanation:
The statement that Standard Deviation (σ) measures the magnitude of potential outcomes is True. Standard deviation is a statistical measure that indicates how much individual measurements in a data set spread out around the mean (average) value. It is calculated as the square root of the variance, which is the average of the squared differences from the mean. When the standard deviation is zero, the data points do not vary from the mean, indicating no variability. As the standard deviation increases, the data points spread out more widely from the mean, suggesting greater variability in the data set.
For example, if we are looking at test scores from different classes, a lower standard deviation would mean that most students scored around the same range, whereas a higher standard deviation would indicate a wider range of scores, with some students scoring much higher or lower than others.
The Student's t-distribution is another concept, which comes into play when dealing with smaller sample sizes. It is similar to the normal distribution but has more variability, hence it is flatter and more spread out at its apex. This distribution acknowledges that with fewer data points, there is more uncertainty about the variability, and hence, estimations about the population parameters are less precise.
In a practical scenario, if Company A and Company B are being compared for employee retention times, and it's noticed that Company A has a higher standard deviation in the time employees remain at the company, it implies more variability in the tenure of employees compared to Company B.