# Sampling

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1 Sampling Theory Dr. T. T. Kachwala  2 Sampling Theory There are two ways in which reliable data or information may be obtained: i. Complete Enumeration Survey (Census Method) ii. Sampling Method  We use Complete Enumeration Survey to examine every  person or item in the population we wish to describe. This method is accurate but costly & time consuming.  Sampling Theory  We use sampling methods, when it is not possible to count or measure every item in the population. Sampling is simply the process of learning about the  population on the basis of the sample drawn from it.  Thus, in the sampling technique instead of every unit of the population, only a  part of the population is studied and the conclusions are drawn on that basis for the entire population.  A sample is not studied for its own sake. The basic objective of its study is to draw inference about the population. In other words, sampling is only a tool which helps to know the characteristics of the population. 3  Characteristics of Population & Sample Mathematically, we can describe samples and populations by using measures such as mean and standard deviation. When these terms describe the characteristics of a sample, they are called statistics. When they describe the characteristics of a population, they are called parameters. A statistic is a characteristic of a sample; a parameter is a characteristic of a  population. In both the cases the objective is the same i.e. to predict the value of the population parameter (   or  ) . We use the following characteristic symbol to differentiate population and sample: Parameters (Population) Statistics (Sample) Population size = N Sample size = n Population mean =   Sample mean = X bar Population S.D =   Sample S.D = s Population proportion of success = p Sample proportion of success = p bar 4

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