# GSEB Class 11 Statistics Notes Chapter 7 Sampling Methods

This GSEB Class 11 Commerce Statistics Notes Chapter 7 Sampling Methods covers all the important topics and concepts as mentioned in the chapter.

## Sampling Methods Class 11 GSEB Notes

Meaning of Population and Sample:
Population:
A set of all units under study is called a population.
Example: Suppose, to study about the production of cotton cloths in India, all textile mills of India is population.

Sample:
A set of units selected from a population on the basis of some definite criteria is called a sample.
Example: Suppose, to study the IQ level of graduate students of Gujarat University, if we select 1000 graduates from all graduate students of Gujarat University on the basis of some criteria, then set of these 1000 graduates is a sample.

Sample With Replacement:
A sample in which each unit is selected from the population after replacing the unit selected earlier in the population is called a Sample With Replacement (SWR).

Sample Without Replacement:
A sample in which each unit is selected from the population without replacing the unit selected earlier in the population is called a Sample Without Replacement (SWOR).

Population Inquiry and Sample Inquiry:
Population Inquiry: The inquiry in which information is collected from each and every unit of the population is called population inquiry or census survey. The census survey conducted every ten years in India is population inquiry.

Sample Inquiry:
The inquiry in which information is collected from a few units selected from the population is called sample inquiry or sample survey. For example, if the information about the annual income of a few families selected from the families residing in Ahmedabad city, is collected, it is sample inquiry.

Sampling:
The procedure of selecting a sample from a population is called sampling. The main objective of sampling is to draw inference about the characteristics of the population on the basis of sample inquiry.

Need of Sampling:
Sampling is an inevitable part of our daily life. Knowingly or unknowingly we make use of sampling in practice. In the following circumstance sampling is inevitable:

• Population is very large
• It is spread over wide geographical area,
• the units under inquiry are to be destroyed,
• The results of inquiry are to be obtained in short period of time and
• Time, money and experts for conducting an inquiry are limited.

Parameters:
Population measures obtained on the basis of population data are called parameters. Population mean standard deviation. Coefficient of skewness etc are population parameter.

Sample Statistics:
The measures of sample obtained from the sample data are called sample statistics. Sample mean, standard deviation, coefficient of skewness etc. are sample statistics.

Characteristics of an Ideal Sample:

• It should be representative of the population.
• It should be free from bias and prejudice.
• The factors affecting its selection should be stable.
• Sample units should be selected in the same period of time.
• Sample units should be selected independently.
• Its size should be adequate.

Points to be considered while determining the Sample Size:

• Purpose of inquiry,
• Size of the population and scope of study,
• Heterogeneity of population
• Availability of time, money and expertise and
• expected level of accuracy of results.

Sampling Methods:
1. Simple Random Sampling:
A sampling in which each unit of the population has an equal chance of being selected in the sample is called a simple random sampling.

• It is convenient when population is homogeneous and the results obtained are reliable.
• Simple Random Sampling With Replacement: If each unit of sample is selected from the population after replacing the unit selected earlier in the population, then such sampling is called simple random sampling with replacement.
• Simple Random Sampling Without Replacement: If each unit of sample is selected from the population without replacing the unit selected earlier in the population, then such sampling is called simple random sampling without replacement.

Methods of obtaining Simple Random Sample:

• Method of Lottery and
• Method of random numbers table.

Popular tables of Random Numbers:

• L.H.C. Tippetâ€™s table of random numbers.
• Tables of Fisher and Yate and
• Tables of Rand Corporation of America.

2. Stratified Random Sampling:
When the population is heterogeneous, it is first divided into different strata of homogeneous nature. A random sample is independently drawn from each stratum and random sample so obtained from all strata are combined to get a sample called a stratified random sample and the method selecting such a sample is called stratified random sampling.

• When the population is heterogeneous, this method is useful
• Stratification: A process of dividing heterogeneous population into non-orver-lapping fairly homogeneous groups is called stratification.
• Stratum: The groups obtained by stratification are called strata, while each group of such groups is called stratum. The strata differ from one another, while each stratum have almost same characteristics. A random sample is drawn from each stratum proportional to the size of stratum.
• Proportional Allocation OR Optimal Allocation or Minimum Cost: It decides how many units are selected from each stratum.

3. Systematic Sampling:
If the complete list of population units is available and the units are arranged in some systematic manner, then this method of sampling is useful. Determining sampling interval k. A random number is selected from the units of sampling interval and select every Jcth unit therefore set of such selected units is called systematic sample and the method of drawing such a sample is called systematic sampling.

• Assigning number 1 to N to the N population units. We have to select a sample of size n.
• Sampling Interval: If N = nk, i.e., k = $$\frac{N}{n}$$ then k is called sampling interval, where k is a positive integer.
• Selecting a unit randomly from 1 to 10 units, every 10th unit is selected thereafter.
• Suppose k = 10, if a number selected randomly from the first 10 units is 7, then every 10th unit is selected thereafter. Thus 7, 17, 27, 37, …, etc. are the units selected in the systematic sample.