Question

A population has a mean of 50 and a variance of 0 (zero). What is the logical conclusion to be drawn from this information?

A) It is an error.
B) The population consists of 50 units.
C) There are no units in the population.
D) All units in the population have the same value of 50.
E) None of the above.

Answer 1

Option (D), The logical conclusion from a population having a mean of 50 and a variance of zero is that all units in the population have the same value, which is 50.

Step-by-step explanation:

When a population has a variance of zero, this implies that standard deviation is also zero, since variance is simply the square of the standard deviation. A variance of zero is only possible if all values in the population are identical; there is no variability among the values.

In the context of the question, where the population mean is 50 and the variance is zero, the logical conclusion is D) All units in the population have the same value of 50.