# Sampling and Sampling Distributions

• ### Examples of Sampling Distribution

Example: Draw all possible samples of size 2 without replacement from a population consisting of 3, 6, 9, 12, 15. Form the sample distribution of sample means and verify the results.             (i)                               (ii)        Solution: We have population values 3, 6, 9, 12, 15, population size and sample size Thus, the number […]

• ### Sampling Distribution

Suppose we have a finite population and we draw all possible simple random samples of size by without replacement or with replacement. For each sample we calculate some statistic (sample mean or proportion etc.). All possible values of the statistic make a probability distribution which is called the sampling distribution. The number of all possible […]

• ### Non Sampling Errors

There are certain sources of errors which occur both in sample survey as well as in the complete enumeration. These errors are of common nature. Suppose we study each and every unit of the population. The population parameter under study is the population mean and the ‘true’ value of the parameter is which is unknown. […]

• ### Sampling Errors

Suppose we are interested in the value of a population parameter, the true value of which is but is unknown. The knowledge about can be obtained either from a sample data or from the population data. In both cases, there is a possibility of not reaching the true value of the parameter. The difference between […]

• ### Simple Random Sampling

Simple random sample (SRS) is a special case of a random sample. A sample is called simple random sample if each unit of the population has an equal chance of being selected for the sample. Whenever a unit is selected for the sample, the units of the population are equally likely to be selected. It […]

• ### Sampling Without Replacement

Sampling is called without replacement when a unit is selected at random from the population and it is not returned to the main lot. First unit is selected out of a population of size and the second unit is selected out of the remaining population of units and so on. Thus the size of the […]

• ### Sampling With Replacement

Sampling is called with replacementwhen a unit selected at random from the population is returned to the population and then a second element is selected at random. Whenever a unit is selected, the population contains all the same units. A unit may be selected more than once. There is no change at all in the […]

• ### Probability and Nonprobability Sampling

The term probability samplingis used when the selection of the sample is purely based on chance. The human mind has no control on the selection or non- selection of the units for the sample. Every unit of the population has known nonzero probability of being selected for the sample. The probability of selection may b […]

• ### Equal Probability and Nonzero Probability

Equal Probability: The term equal probability is frequently used in the theory of sampling. This term is quite often not understood correctly. It is thought to be close to ‘equal’ in meaning. It is not true always. Suppose there is a population of 50(N = 50) students in a class. We select any one student. […]

• ### Sample Design and Sampling Frame

Sample Design: In sample studies, we have to make a plan regarding the size of the sample, selection of the sample, collection of the sample data and preparation of the final results based on the sample study. The whole procedure involved is called the sample design. The term sample survey is used for a detailed […]

• ### Limitations of Sampling

Sometimes the information about each and every unit of the population is required. This is possible only through the complete enumeration because the sample will not serve the purpose. Some examples in which the sampling is not allowed are: To conduct the elections, we need a complete list of the votes. The candidates participating in […]

• ### Sample Survey and Advantages of Sampling

If it is not essential to conduct the complete enumeration, then a sample of some suitable size is selected form the population and the study is carried out on the sample. This study is called sample survey. Most of the research work is done through sample surveys. The opinion of the voters in favor of […]