What is Sampling?
Sampling is a method used in statistical analysis in which a decided number of considerations are taken from a comprehensive population or a sample survey. The methodology used to sample from an extensive population depends on the type of study being conducted but may involve simple random sampling or systematic sampling.
Methods Of Sampling
Random Sampling
Q.1Define random sampling. Discuss its merits and demerits. 
Answer: 
(A) Random Sampling 
 Random sampling method refers to a method in which every item in the universe has an equal chance of being selected.
 It is also known as Probability Sampling or Representative Sampling.
 There is no room for discrimination in random sampling

(B) Following Are The Merits Of Random Sampling: 
(1) No Personal Bias 
 Selection of various items in the sample remains free from the personal bias of the investigator.

(2) Based On Probability 
 Due to the random character of the sample, the rules of probability are applicable.

(3) Increasingly Representative Of The Population 
 As the size of a random sample increases, it becomes more and more representative of the population.

(4) Accuracy Can Be Assessed 
 The accuracy can be assessed with the help of the magnitude of sampling errors.

(c) Following are some of the demerits of random sampling: 
(1) Not Suitable For Small Samples 
 It may not reflect the true characteristics of the population if the sample is small.

(2) Difficult To Prepare Sampling Frame 
 The selection of a random sample requires the preparation of a Sampling Frame, which may be difficult for a large or an infinite population.

Short Answer Questions: Types of Random Sampling
Q.1Explain the different types of random sampling. Also, list the methods covered under each category. 
Answer: 
There are two types of random sampling:
 Simple or unrestricted random sampling
 Restricted random sampling

(A) Simple Random Sampling
(Unrestricted Random Sampling) 
 A Simple Random Sample is one in which every item of the population has an equal chance of being selected.
 This method is also known as Unrestricted Random Sampling.
 Instead of Investigator, Process used decides the chances of selection of an item.
 Under this type of Random Sampling, samples are selected by using the following two methods:
 Lottery Method
 Table of Random Numbers

(B) Restricted Random Sampling 
 In the case of the heterogeneous population when samples are selected randomly but under certain restrictions, it is termed as Restricted Random Sampling.
 It involves the personal attention of the investigator while selecting a sample.
 It is not purely random.
 Important Methods under this category are: i. Stratified Random Sampling. ii. Systemic Sampling. iii. Cluster or Multistage Sampling.

Students can also refer to What are the Sources of Data?
Short Answer Questions: Restricted Random Sampling
Q.1Briefly explain the following methods/techniques of restricted random
Sampling:
(a) Stratified random sampling
(b) Systemic sampling
(c) Cluster or multistage sampling. 
Answer: 
(A) Stratified Random Sampling 
 In this method, the universe or the entire population is divided into ‘Strata’ i.e. a number of homogenous groups and then from each ‘Stratum’ or group certain numbers of items are taken at random.
 For example, in a class of 40 students to select two Monitors randomly first of all students are divided into two homogeneous groups i.e. Boys and Girls and then they are one each is selected from them randomly.
 Merits:
 Sample taken is more representative of the universe.
 It is easier to organize and administer because the universe is subdivided.
 It ensures greater accuracy because each group contains uniform items.
 Not possible if information about the population or ‘Strata’ is not available.
 If stratification is not done properly, the purpose will not be served.

(B) Systematic Sampling 
 It is also known as QuasiRandom Sampling.
 Under this method, the whole population is arranged ‘Alphabetically’ or ‘Geographically’, or ‘Numerically’ or in some other systematic order.
 Then every ‘n^{th}’ item is selected as a sample item. Where ‘n’ stands for any number.
 Like, every ‘Even item’ or every ‘3^{rd} /4^{th} /5^{th} ….Item’.
 For better results, a list of items should be fully random and the first items should be selected using simple random sampling method.
 Merits:
 It is a very simple method and generally, results are satisfactory.
 Rechecking can be done quickly.
 Same time and efforts.
 Possible only if the complete list of items is available.
 Feasible only if units are systematically arranged.
 Chances of bias are there.

(C) Cluster Sampling
Or
Multistage Sampling 
 It involves the procedure of dividing the large population into groups called clusters and drawing a sample of clusters to represent the population.
 It is carried out in multiple stages say, two, three or four stages.
 In the first stage – The universe is divided into many clusters from which certain clusters are selected at random as the first stage samples.
 In the second stage – The selected first stage samples are again subdivided into some clusters from which again, certain clusters are selected at random as the second stage samples.
 In the third stage – The selected second stage samples are again subdivided into some clusters from which certain clusters are again selected at random as the third stage samples.
 Process of division and subdivision of clusters and selection of multistage samples is carried out until the sample size is reduced to a reasonable extent.
 Merits:
 Very helpful in large scale surveys.
 Represents the population with reasonable accuracy.
 Saves time and money.
 Division of population into clusters and subclusters is quite a difficult task.
 The investigator needs to have detailed knowledge about the universe expertise in division and selection of clusters.

NonRandom Sampling
Q.1What do you understand by nonrandom sampling? Name the various methods of nonrandom sampling. 
Answer: 
(A) Nonrandom Sampling 
 Nonrandom sampling is one in which all the items of the universe do not have equal chances of being selected.
 Investigator selects samples on the basis of convenience or his judgment rather than on the basis of probability.

(b) Following are the main methods of nonrandom sampling: 
(1) Judgement Sampling 
 Under this method, the choice of sample items depends exclusively on the judgment of the investigator.
 On the basis of his own choice, he tries to select the best representative of the whole population.
 It is also known as Purposive and Deliberate Sampling.
 For example:
 If a music teacher has to select five students from his school for participation in interschool competition. She cannot use random sampling method.
 In this case, she will use her own judgment to select those five students from a big lot.
 Merits:
 Useful where the personal judgment of the investigator is important.
 Where the smallsized sample is to be drawn.
 Where some characteristics are to be observed in detail.
 Not based on probability, it doesn’t guarantee accuracy.
 Selection of items may be affected by personal bias or prejudice.

(2) Quota Sampling 
 Under this method, the items of the population are subdivided into various groups and then a quota (number of items to be selected from each subgroup) is fixed.
 But, within the given quota, selection of sample units depends upon the personal judgment of the investigator. So, this is a kind of Judgment Sampling only.
 For example:
 In a survey of Reliance Jio network users, the interviewers may be told to interview 100 people living in a certain area.
 Out of those 100, 60% of the interviewed are to be working people, 30% should be students, and others to be 10%.
 Within these quotas, the interviewer is free to select the people to be interviewed.
 Merits:
 Provides satisfactory results if Quotas are allocated objectively.
 Each part of the population gets representation.
 Satisfactory results are expected.
 This method is subject to personal bias.
 Proves useful only if Interviewers are properly trained.

(3) Convenience Sampling 
 Under this method, while selecting the sample units, the investigator gives special attention to his convenience.
 For example:
 To estimate the average height of an Indian, the investigator (belonging to Delhi) can take a convenience sample from the Delhi State only and estimate the average height of an Indian.
 This method of selecting the sample is also called ‘Chunk’.
 Merits:
 Useful when the universe is not properly defined.
 The economy of time, money and efforts.
 Sample items may not truly represent the universe.
 Results obtained are often less reliable.

Reliability of Sampling & Statistical Errors
Q.1What is the law of statistical regularity? 
Answer: 
Law Of Statistical Regularity 
 This law says, if a random sample of adequate size is selected from a large population, it tends to possess the same characteristics as those of the population.

Q.2State the law of inertia of large number. 
Answer: 
Law Of Inertia Of Large Numbers 
 According to this law, the aggregates or averages obtained from a large group are more stable than the aggregates or average obtained from a smaller group.
 In other words, large the size of the sample, more accurate the results are likely to be.

Q.3What is meant by statistical errors? Explain different types of Statistical errors. 
Answer: 
(A) Statistical Errors 
 The statistical error refers to the difference between the collected data and the actual value of facts.
 In other words, it is the difference between the estimated value and the actual values taken by the investigator.

(b) Following are the different types of errors 
(1) Sampling Errors 
Sampling Error
 It refers to the differences between the sample estimate and the actual value of a characteristic of the population.
 Sampling Errors can be of two types: Biased Error: An error which arises on account of some bias or imbalance on the part of the Investigator, Informants or Instruments of counting, measurement or experiment is called Biased Error. Unbiased Error: An error which does not take place on account of any bias with anybody but occurs accidentally may be due a chance or due to an arithmetic error is called Unbiased Error. Such errors arise automatically without any motive.
 The magnitude of Sampling Error can be reduced by taking a larger sample.

(2) Nonsampling Errors 
Nonsampling Error
 These errors occur in acquiring, recording or tabulating statistical data.
 These are more serious than sampling errors because a sampling error can be minimized by taking a large sample.
 But, a nonsampling error cannot be minimized even by taking a large sample

The abovementioned concept is for CBSE class 11 Statistics for What are the Types of Sampling Methods. For solutions and study materials for class 11 Statistics, visit BYJU’S or download the app for more information and the best learning experience.