Standard deviation sampling distribution

The device or process of selecting a small part from n aggregate population is called sampling for example in a grain market if a customer takes a handful of wheat to find out the quality of that lot, then the small selected part is called sample and the process of selection is called sampling..

BASIC CONCEPT

Introduction: All of us are familiar with the idea of sampling in every day life. For example the cook tastes a bit of cooked food to see whether it as been properly cooked. The customer by observation samples the quality of fruits and vegetable he intends to buy . A food inspector takes a sample food items like milk floor etc to find out whether they are pure or not The medical doctors receive samples of various medicines to determine their effectiveness.

Definition: Sampling is a process of selecting a part of aggregate of material in the belief that the part selected will exhibit the relevant characteristics of the whole aggregate. This representative part in statistical terminology, is called a sample and the whole aggregate from which the sample is draw is called"population" or universe.

The production of different things in mills from population of production etc these units objects which are of the same kind and which van be numerically specified are called sampling units or elements.

There are two types of sampling unit in which one is individual and other one is cluster.

SAMPLING DISTRIBUTION: The probability distribution or relative frequency distribution of the values of statistics is called sampling distribution of that statistic.

The probability distribution of the values of a statistic computed from all possible samples of size "n" that can be drawn either with or with out replacement from a population of size N is called sampling distribution.

Since sampling distribution is a probability distribution therefore total probability must be equal to one.

STANDARD EROOR: The standard deviation of the sampling distribution of a statistics is called standard error of that statistics.

The difference between standard error and standard deviation is that standard error measures the dispersion in the values of a statistics while the standard deviation measures that dispersion in population or sample data

PROPORTION: The probability distribution of the values of sample proportion of success P^{^} is called sampling distribution of sample proportion.

The probability distribution of the values of sample proportion P^{^} computed from all possible samples of size n that can be drawn either with or with out replacement from a binomial probability of size N is called sampling distribution of sample proportion.