From a population of size 500, a random sample of 50 items is selected. The mode of the sample
A) must be 500.
B) must be equal to the mode of population, if the sample is truly random.
C) must be equal to the mean of the population, if the sample is truly random.
D) can be larger, smaller or equal to the mode of the population.

Question

Quizplus · Accepted Answer

The mode of the sample is not necessarily the same as the mode of the population. It can be larger, smaller or equal, depending on chance. The mode of the sample is simply the most frequently occurring value in the sample, while the mode of the population is the most frequently occurring value in the entire population. Since the sample is selected randomly, there is no guarantee that the mode of the sample will be the same as that of the population.

From a Population of Size 500, a Random Sample of 50