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. For sampling, the methodology used from an extensive population depends on the type of study being conducted; but may involve simple random sampling or systematic sampling.
Methods of Sampling
|Q.1 Define random sampling. Discuss its merits and demerits.|
|(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) The merits of random sampling are as follows:
|(1) No personal bias||● The 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) Increasing 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) The demerits of random sampling are as follows:|
|(1) Not suitable for small samples||● If the sample is small, it may not reflect the true characteristics of the population.|
|(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.1 Explain the different types of random sampling. List the methods covered under each category.|
|There are two types of random sampling.
|(A) Simple random sampling
(Unrestricted random sampling)
|● A simple random sampling 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.
● The process used decides the chances of selection of an item, not an investigator.
● Under this type of random sampling, the samples are selected by using the following two methods:
|(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 as follows:
i. Stratified random sampling
ii. Systematic sampling
iii. Cluster or multistage sampling
Students can also refer: What are the Sources of Data?
Short Answer Questions: Restricted Random Sampling
|Q.1 Briefly explain the following methods/techniques of restricted random
(a) Stratified random sampling
(b) Systematic sampling
(c) Cluster or multistage sampling
|(A) Stratified random sampling||● In this method, the universe or the entire population is divided into ‘strata’, i.e., a number of homogenous groups. Then from each ‘stratum’ or group, a certain number of items are taken at random.
● Example: To select two monitors randomly in a class of 40 students. First of all students are divided into two homogeneous groups, i.e., boys and girls and then each one is selected from them randomly.
|(B) Systematic sampling||● It is also known as quasi-random sampling.
● Under this method, the whole population is arranged ‘alphabetically’, ‘geographically’, ‘numerically’, or in some other systematic order.
● Then every ‘nth’ item is selected as a sample item. Where ‘n’ stands for any number.
● Like, every even or odd item.
● For better results, a list of items should be completely random and the first items should be selected using a simple random sampling method.
|(C) Cluster sampling
|● It involves the procedure of dividing the large population into groups known as 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.
● The 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.
|Q.1 What do you understand by non-random sampling? Name the various methods of non-random sampling.|
|(A) Non-random sampling||● Non-random sampling is one in which all the items of the universe do not have equal chances of being selected.
● The investigator selects samples on the basis of convenience or his judgment rather than on the basis of probability.
|(b) The main methods of non-random sampling are as follows:
|(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.
● If a music teacher has to select five students from his/her school for participation in an inter-school competition. He/She cannot use a random sampling method.
● In this case, he/she will use his/her own judgment to select those five students from a big lot.
|(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 sub-group) is fixed.
● However, within the given quota, the selection of sample units depends upon the personal judgment of the investigator. So, this is a type of judgment sampling only.
● 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.
|(3) Convenience sampling||● Under this method, while selecting the sample units, the investigator gives special attention to his convenience.
● To estimate the average height of an Indian, the investigator (belonging to Delhi) can take a convenience sample from Delhi only and estimate the average height of an Indian.
● This method of selecting the sample is also known as ‘chunk’.
Reliability of Sampling and Statistical Errors
|Q.1 What is the law of statistical regularity?|
|Law of statistical regularity||● The law states that 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.2 State the law of inertia of large numbers.|
|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, larger the size of the sample, more accurate the results are likely to be.
|Q.3 What is meant by statistical errors? Explain different types of statistical errors.|
|(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) The different types of errors are as follows:|
|(1) Sampling errors||Sampling error
● It refers to the differences between the sample estimate and the actual value of the characteristics of the population.
● Sampling errors can be of two types.
● Biased error: An error that arises on account of some biases or imbalances on the part of the investigators, informants, or instruments of counting, measuring, or experimenting is known as a biased error.
● Unbiased error: An error that does not take place on account of any bias with anybody but occurs accidentally may be due to a chance or due to an arithmetic error is known as an unbiased error. Such errors arise automatically without any motive.
● The magnitude of sampling error can be reduced by taking a larger sample.
|(2) Non-sampling errors||Non-sampling error
● These errors occur in acquiring, recording, or tabulating statistical data.
● These are more serious than sampling errors because a sampling error can be minimised by taking a larger sample.
● However, a non-sampling error cannot be minimised even by taking a larger sample.
The mentioned concept is for CBSE class 11 statistics for ‘What are the Types of Sampling Methods?’. For solutions, study materials, and more information for class 11 statistics, visit BYJU’S website or download the app and get the best learning experience.