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BBA/BCM 2 All right are reserved with CU-IDOL Business Mathematics and Statistics Course Code: BBA/BCM 102 Semester: First SLM Unit: 12,13 E-Lesson: 6 www.wcwuiwd.ocul.iidnol.in Unit -12,13(BBA /BCOM -101)

Business Mathematics and 33 Statistics OBJECTIVES INTRODUCTION To make students aware of the basic concepts of In this unit we are going to learn about the sampling. concept and applicability of sampling. To develop an understanding of the difference Under this you will learn and understand the between census and sampling. difference between census and sampling. To make students understand the types of In this unit you will learn the types of probability and non probability sampling. probability and non probability sampling. www.wcwuiwd.ocul.iidnol.in Unit -12,133(BBBAA/B/BCCMOM10-2101)INSTITUTE OF DISTAAllNCriEgAhNt aDreONreLsINerEvLeEdAwRNithINCGU-IDOL

Topics To Be Covered 4 Basic Terminologies Introduction of Sampling Introduction of Census Difference between census and sampling Types of probability and non-probability sample www.cuidol.in Unit -12,13(BBA /BCOM -101) All right are reserved with CU-IDOL

Basic Terminologies Population or Universe: It refers to the group of people, items or units under investigation and 5 includes every individual. Sample: The items taken from the population for analysis (for deduction of hypothesis or arriving at a conclusion) are samples. Unit: Each component of the population being studied is known as a unit of the population. Some or many of these units are chosen as samples for further analysis and deduction. Sample Frame: The collection of the elements from which samples are drawn is known as Sample Frame. Sample Frame can be the same as Population or a part of the Population in some cases. Sample Frame must be significantly larger than the Sample Size to obtain higher level of accuracy in our results. The Sample Frame must be representative of the whole population. Sample Size: The size of the total samples to be taken constitutes the sample size. This is the collection of all the samples taken. Sampling: It is the process of selecting a sample from the population. www.cuidol.in Unit -12,13(BBA /BCOM -101) All right are reserved with CU-IDOL

Introduction Sampling is the statistical process of selecting a subset 6 (called a “sample”) of a population of interest for purposes All right are reserved with CU-IDOL of making observations and statistical inferences about that population. The sampling method is the one in which only some of the representative items of the population are selected and data are collected from these. Instead of collecting information for and from all the units of population, we select a sample i.e. only a few items of the population. Conclusions derived from the small sample are generalized for the whole population. For example- A doctor examines a few drops of blood as a sample and draws a conclusion about the blood constitution of the whole body www.cuidol.in Unit -12,13(BBA /BCOM -101)

Need of Sampling 7 1. Large population can be conveniently covered. 2. Time, money and energy is saved. 3. Helpful when units of area are homogenous. 4. Used when percent accuracy is not acquired. 5. Used when the data is unlimited. www.cuidol.in Unit -12,13(BBA /BCOM -101) All right are reserved with CU-IDOL

Advantages of Sampling 8 1. Economical: Reduce the cost as compared to entire population. 2. Increased speed: Collection of data, analysis and interpretation of data takes less time than the population. 3. Accuracy: Due to limited area of coverage, completeness and accuracy is possible. 4. Rapport: Better rapport is established with the respondents, which helps in validity and reliability of the results. www.cuidol.in Unit -12,13(BBA /BCOM -101) All right are reserved with CU-IDOL

Disadvantages of Sampling 9 1. Biasness: Chances of biased selection leading to incorrect conclusion. 2. Selection of true representative sample: Sometimes it is difficult to select the right representative sample. 3. Need for specialized knowledge: The researcher needs knowledge, training and experience in sampling technique, statistical analysis and calculation of probable error. 4. Impossibility of sampling: Sometimes population is too small or too heterogeneous to select a representative sample. www.cuidol.in Unit -12,13(BBA /BCOM -101) All right are reserved with CU-IDOL

Characteristics of a Good 10 Sample A true representative of the population. Free from error due to bias. Adequate in size for being reliable. Units of sample should be independent and relevant. Units of sample should be complete precise and up to date. Free from random sampling error. Avoiding substituting the original sample for convenience. www.cuidol.in Unit -12,13(BBA /BCOM -101) All right are reserved with CU-IDOL

Census- Introduction 11 Definition- A census is a survey conducted on the full set of observation objects belonging to a given population or universe. Census method is that process of the statistical list where all members of the population are analyzed. A population relates to the set of all observations under concern. For instance, if we want to carry out a study to find out student’s feedback about the amenities of the school, all the students of the school would form a component of the ‘population’ for the study. www.cuidol.in Unit -12,13(BBA /BCOM -101) All right are reserved with CU-IDOL

Advantages and 12 Disadvantages of Census Method ADVANTAGES OF CENSUS METHOD DISADVANTAGES OF CENSUS METHOD Intensive study- It provides intensive and in- Costly method- Since the data are obtained depth information covering many facets of the for or from each & every unit of the population, problems. it is a very expensive method of investigation, especially in case of large size of the Results are more accurate and reliable- population. Since in this type of investigation every item of the universe is taken into account, the Needs more time and manpower- Since a conclusions are more accurate and reliable. large volume of data is to be collected, more time and manpower is required for its collection, analysis and interpretation. Not suitable for the large population- This method is meaningless in case of an infinite universe where the number of items is unlimited. www.cuidol.in Unit -12,13(BBA /BCOM -101) All right are reserved with CU-IDOL

Census VS Sampling BASIS FOR COMPARISON CENSUS SAMPLING 13 Meaning A systematic method that collects Sampling refers to a portion of the Enumeration and records the data about the population selected to represent Study of members of the population is the entire group, in all its Time required called Census. characteristics. Cost Results Complete Partial Error Each and every unit of the Only a handful of units of the Appropriate for population. population. www.cuidol.in It is a time consuming process. It is a fast process. Expensive method Economical method Reliable and accurate Less reliable and accurate, due to the margin of error in the data collected. Not present. Depends on the size of the population Population of heterogeneous Population of homogeneous nature. nature. Unit -12,13(BBA /BCOM -101) All right are reserved with CU-IDOL

Classification of Sampling 14 Techniques www.cuidol.in Unit -12,13(BBA /BCOM -101) All right are reserved with CU-IDOL

Types of Sampling In Statistics, there are different sampling techniques available to get relevant results from the population. 1 5 The two different types of sampling methods are: Probability Sampling: The probability sampling method utilizes some form of random selection. In this method, all the eligible individuals have a chance of selecting the sample from the whole sample space. This method is more time consuming and expensive than the non-probability sampling method. The benefit of using probability sampling is that it guarantees the sample that should be the representative of the population. Non-Probability Sampling: The non-probability sampling method is a technique in which the researcher selects the sample based on subjective judgment rather than the random selection. In this method, not all the members of the population have a chance to participate in the study. In Non-probability sampling, it relies on personal judgment. www.cuidol.in Unit -12,13(BBA /BCOM -101) All right are reserved with CU-IDOL

Types of Probability 16 Sampling www.cuidol.in Unit -12,13(BBA /BCOM -101) All right are reserved with CU-IDOL

Types of Probability 17 Sampling Simple Random Sampling In simple random sampling technique, every item in the population has an equal and likely chance of being selected in the sample. Since the item selection entirely depends on the chance, this method is known as “Method of chance Selection”. As the sample size is large, and the item is chosen randomly, it is known as “Representative Sampling”. For Example: If we wish to draw a sample of 50 students from a population of 400 students. Place all 400 names in a container and draw out 50 names one by one. www.cuidol.in Unit -12,13(BBA /BCOM -101) All right are reserved with CU-IDOL

Systematic Sampling 18 In systematic sampling method, the items are selected from the target population by selecting the random selecting point and selecting the other methods after a fixed sample interval. It is calculated by dividing the total population size by the desired population size. For Example: for a sample of 50 students, the sampling fraction is 50/400 = 1/8 i.e. select one student out of every eight students in the population. The starting points for the selection is chosen at random. www.cuidol.in Unit -12,13(BBA /BCOM -101) All right are reserved with CU-IDOL

Cluster sampling 19 In the cluster sampling method, the cluster or group of people are formed from the population set. The group has similar significatory characteristics. Also, they have an equal chance of being a part of the sample. This method uses simple random sampling for the cluster of population. For example: The study involves Primary schools. Select randomly 15 schools. Then study all the children of 15 schools. In cluster sampling the unit of sampling consists of multiple cases. It is also known as area sampling, as the selection of individual member is made on the basis of place residence or employment. www.cuidol.in Unit -12,13(BBA /BCOM -101) All right are reserved with CU-IDOL

Types of Non-Probability 20 Sampling www.cuidol.in Unit -12,13(BBA /BCOM -101) All right are reserved with CU-IDOL

21 Purposive Sampling Purposive sampling is also known as judgmental sampling. In this technique, researcher selects sample on the basis of his/her prior experience or belief that certain candidates will be suitable for the particular study. Researchers would like to go with their judgment regarding selection of sample. www.cuidol.in Unit -12,13(BBA /BCOM -101) All right are reserved with CU-IDOL

Convenience Sampling 22 Convenience sampling is probably the most common of all sampling techniques. With convenience sampling, the samples are selected because they are accessible to the researcher. Subjects are chosen simply because they are easy to recruit. This technique is considered easiest, cheapest and least time consuming. In selecting the incidental sample, the researcher determines the required sample size and then simply collects data on that number of individuals who are available easily. www.cuidol.in Unit -12,13(BBA /BCOM -101) All right are reserved with CU-IDOL

Quota Sampling 23 All right are reserved with CU-IDOL Quota sampling is a non-probability sampling technique wherein the researcher ensures equal or proportionate representation of subjects depending on which trait is considered as basis of the quota. For example – researcher wants to study pizza lover males and females in a society where 2500 individuals (1500 males and 1000 females) are staying. He first identifies the sub-groups (strata) of male and female. Then researcher chooses the sample units by judgment or convenience from each group based on specified proportion. www.cuidol.in Unit -12,13(BBA /BCOM -101)

Snowball Sampling 24 All right are reserved with CU-IDOL Snowball sampling is also known as network sampling or chain-referral sampling. This technique is used when features need to be studied are rare and difficult to find. In this technique, samples are created through chain referrals. Subjects refer the researcher to others who might be recruited as subjects. This technique is useful when study participants are difficult to identify, locate or access. One or more identified sample can recommend others for the study. For example – researcher wants to study the experiences of individuals who spent long time in the jail. Researcher may not get enough sample in such cases but if researcher manages to get one candidate for study. That candidate can further refer other suitable individuals for the study. www.cuidol.in Unit -12,13(BBA /BCOM -101)

Summary 25 Population- Population is the collection of the elements which has some or the other characteristic in common. Number of elements in the population is the size of the population. Sample- Sample is the subset of the population. The process of selecting a sample is known as sampling. Number of elements in the sample is the sample size. Census Method- The Census Method is also called as a Complete Enumeration Survey Method wherein each and every item in the universe is selected for the data collection. The universe might constitute a particular place, a group of people or any specific locality which is the complete set of items and which are of interest in any particular situation. Probability sampling- Probability sampling is a sampling technique wherein the samples are gathered in a process that gives all the individuals in the population equal chances of being selected. Non-Probability Sampling- Non-probability sampling is a sampling technique where the samples are gathered in a process that does not give all the individuals in the population equal chances of being selected. It does not rely on randomization. This technique is more reliant on the researcher’s ability to select elements for a sample. Outcome of sampling might be biased and makes difficult for all the elements of population to be part of the sample equally. This type of sampling is also known as non- random sampling. www.cuidol.in Unit -12,13(BBA /BCOM -101) All right are reserved with CU-IDOL

Multiple Choice Questions 26 1 Sample is a sub-set of: (c) Set (a) Population (d) Distribution (b) Data 2 Study of population is called: (c) Error (a) Parameter (d) Census (b) Statistic 3 Random sampling is also called: (c) Sampling error (a) Probability sampling (d) Random error (b) Non-probability sampling Answers: 1.(a) 2.(d) 3. (a) www.cuidol.in Unit -12,13(BBA /BCOM -101) All right are reserved with CU-IDOL

Frequently Asked Questions 27 Q1 What is sampling? Ans: Sampling is the selection of a subset (a statistical sample) of individuals from within a statistical population to estimate characteristics of the whole population. Q2 What is probability sampling? Ans: Probability sampling is based on the fact that every member of a population has a known and equal chance of being selected. Q3 What is non probability sampling? Ans: Non-probability sampling is a sampling technique where the samples are gathered in a process that does not give all the individuals in the population equal chances of being selected. Q4 What is Simple random sampling? Ans: Simple random sampling is a completely random method of selecting subjects. These can include assigning numbers to all subjects and then using a random number generator to choose random numbers. Classic ball and urn experiments are another example of this process (assuming the balls are sufficiently mixed). The members whose numbers are chosen are included in the sample. www.cuidol.in Unit -12,13(BBA /BCOM -101) All right are reserved with CU-IDOL

REFERENCES 28 1. Gupta, S.P. and Gupta M.P. (2017). Business Statistics. New Delhi: Sultan Chand & Sons. 2. Aggarwal, S.C. and Jain, T.R. (2008).Business Statistics. New Delhi: V.K. Publications. 3. Vohra , N.D. (2014). Business Mathematics and Statistics. New Delhi: MC Graw Hill Education Pvt. Ltd. www.cuidol.in Unit -12,13(BBA /BCOM -101) All right are reserved with CU-IDOL

29 THANK YOU For queries Email: [email protected] www.cuidol.in Unit -12,13(BBA /BCOM -101) All right are reserved with CU-IDOL

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