Question

5) Explain the differences between the population distribution, the distribution of a sample, and a sampling distribution. Describe each of these in a single context of your choosing.

Answer 1

Population Distribution:

The population is the whole set of values, or individuals, you are interested in. For example, if you want to know the average height of the residents of India, that is your population, ie, the population of India.

Population characteristic are mean (μ), Standard deviation (σ) , proportion (P) , median, percentiles etc. The value of a population characteristic is fixed. This characteristics are called population distribution. They are symbolized by Greek characters as they are population parameters.

Sample Distribution:

The sample is a subset of the population, and is the set of values you actually use in your estimation. Let’s think 1000 individual you have selected for your study to know about average height of the residents of India. This sample has some quantity computed from values e.g. mean (x ), Standard deviation (s) , sample proportion etc. This is called sample distribution. The mean and standard deviation are symbolized by Roman characters as they are sample statistics.