This document discusses different methods of sampling, including simple random sampling, systematic sampling, and sampling with unequal probabilities. It provides examples to illustrate each method. The purpose of sampling is to make inferences about a whole population by examining a small sample. Sampling provides statistical information about a population more efficiently and quickly than a complete census. While sampling has advantages in cost, time, and scope compared to a full survey, it also has limitations such as potential for high errors with small samples or when very high accuracy is required.

1. Sampling and methods of doing sampling
Basic Concepts Of Sampling
With a single grain of rice, an Asian housewife tests if all the rice in the pot has boiled; from a
cup of tea, a tea-taster determines the quality of the brand of tea; and a sample of moon rocks
provides scientists with information on the origin of the moon. This process of testing some
data based on a small sample is called sampling.
Sampling is the process by which inference is made to the whole by examining a part.
Purpose of Sampling
The purpose of sampling is to provide various types of statistical information of a qualitative or
quantitative nature about the whole by examining a few selected units. The sampling method is
the scientific procedure of selecting those sampling units which would provide the required
estimates with associated margins of uncertainty, arising from exam
Methods of Sample Selection
Simple Random Sampling
In this method each item of the data (population) has the same probability of being selected in
the sample. The selection is usually made with the help of random numbers.
Suppose there are N=850 students in a school from which a sample of n=10 students is to
be taken. The students are numbered from 1 to 850. Since our data runs into three digits
we use random numbers that contain three digits. All numbers exceeding 850 are ignored
because they do not correspond to any serial numbers in the data. In case the same
number occurs again, the repetition is skipped.

2. Systematic Sampling
In this method first we have to number the data items from 1 to N. Suppose the sample size be n,
then we have to calculate the sampling interval by dividing N by n. And generate a number
between 1 and N/n and select that data item to be in the sample. Other items in the sample are
obtained by adding the sampling interval N/n successively to the random number.
Advantage of this method is that the sample is evenly distributed over the entire data.
The town of Fairfax is divided up into N = 576 blocks which are numbered
consecutively. A 10 percent sample of blocks is to be taken, which gives a sampling
interval of k = 10. If the random number between 1 and 10 is 3, the blocks with the
numbers
03, 13, 23, 33, 43... 573 are in the sample.
Sampling with unequal probabilities
When the data items vary considerably in size, a simple random or a systematic random sample
of items does not produce a good estimate due to high variability. In such a situation we get a
better estimate by giving higher probability of selection to the larger data items.
Applications of sampling techniques
Major TV networks rely on surveys to tell them how many and what types of people are
watching their programs.
The U.S. Bureau of Census conducts a survey every month to obtain information on
employment and unemployment in the nation.
Local housing authorities make surveys to ascertain satisfaction of people in public
housing with their living accommodations.
Local transportation authority’s conduct surveys to acquire information on people's
commuting and travel habits.
Magazines and trade journals utilize surveys to find out what their subscribers are
reading.
Surveys are used to ascertain what sorts of people use our national parks and other
recreation facilities.
Auto manufacturers use surveys to find out how satisfied people are with their cars.

3. Advantages of Sampling
Greater economy: The total cost of a sample will be much less than that of the whole lot.
Shorter time-lag: With smaller number of observations it is possible to provide results
much faster as compared to the total number of observations.
Greater scope: Sampling has a greater scope regarding the variety of information by
virtue of its flexibility and adaptability.
Actual appraisal of reliability
Limitations of sampling
Errors due to sampling may be high for small administrative areas.
Sampling may not be feasible for problems that require very high accuracy