Final answer:
The statement is false because the sample standard deviation typically uses Bessel's correction, dividing by n - 1, which differentiates it from the population standard deviation that divides by N, the size of the population.
Step-by-step explanation:
The population standard deviation and sample standard deviation are not necessarily the same value for the same set of data. This statement is false. When calculating the standard deviation for a sample, we divide by n - 1 where n is the sample size. This is known as Bessel's correction, and it is used to provide an unbiased estimate of the population standard deviation based on sample data. On the other hand, the population standard deviation divides by N, which is the size of the entire population. Therefore, the values are different unless the sample size is very large where the difference becomes negligible.
Moreover, it's important to understand that if a data set has a standard deviation equal to zero, it means that all of the data have the same value ). It does not necessarily mean that all values of the data appear with the same frequency or that the mean of the data is zero, only that there is no variability within the data.