Question

4. Explain the differences between the population distribution, the distribution of a sample, and a sampling distribution., use a sample to described it.

Answer 1

Population Distribution is a form of probability distribution that measures the frequency with which the variables that make up the population are drawn for a given research study.

The sample is the representative of the population from where it is drawn. The distribution of a sample measures the frequency with which the number of subjects that make up the sample is actually drawn for a given research study.

The sampling distribution of a statistic is the distribution of that statistic, considered as a random variable, when derived from a random sample size n.

EXAMPLE:
Consider a research study involving average height of all the 2000 students of a college.

The distribution of the height of all the 2000 students is the population distribution.

Suppose we draw a sample of 100 students from this population. The distribution of heights of these 100 students is the distribution of a sample.

Suppose we draw a sample of size n from this population. The distribution of the average height of 100 students of each of the n samples is the sampling distribution of the statistic.