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5.1 Concept of Population and Sample Population: When we think of the term “population,” we usually think of people in our town, region, state or country. However, in statistics, the term “population” takes a slightly different meaning. In statistics, “population or universe” is the aggregate of objects in any statistical investigation. That is, statistical population refers the totality or aggregate of all units or items under investigation or study. In other words, the group of items or units under the study (investigation or inquiry) is called population. There are two types of population. They are target population and sampling population. The population or universe may be finite or infinite. A population containing a finite number of objects or items is known as finite population. For example, total no. of students of T.U in BCA, the total number of books in a library, total number of households in Kathmandu etc. On the other hand, a population having an infinite number of objects is called infinite population. For example, the population of stars in the sky is an infinite population, total number of fishes in Pacific Ocean, total number of trees in a forest etc. In the statistical investigation, the investigator usually deals with the general magnitude and the study of variation respect to one or more characteristics relating to individual belonging to a group. The group of individuals under study is called population or universe. Population is an aggregate or collections of objects, animates or inanimate defined according to characteristics under study. The population may be finite or infinite. Complete enumeration of all units of the population is called census. In any statistical investigation complete enumeration is not practicable. In a statistical investigation the interest usually lies in the assessment of the general magnitude and the study of variation with respect to one or more characteristic relating to individuals under study is called population or universe. Thus, in statistics, population is an aggregate of objects under study. It is obvious that for any statistical investigation complete enumeration of the population is rather impractical. For example, if we want to have an idea of the average per capita (monthly) income of the people of Nepal, we will have to enumerate all the earning individuals in the country, which is rather a very difficult task. If population is infinite, complete enumeration is not possible. Also, if the units are destroyed in the course of inspection, 100% inspection is not taken because of multiplicity of cause, viz., administrative and financial implications, time factors etc. and we take the help of sampling. Sample: A finite subset of statistical individuals in a population that is used to represent that population is called a sample (or the representative part of any population under study is a sample) and the number of individuals in a sample is called sample size. For the purpose of determining population characteristic, instead of enumerating entire population, the individual in the sample only are observed. Then the sample characteristics are utilized to approximately determine or estimate the population. For example, on examining the sample of a particular stuff we arrive at a decision of purchasing or reject the stuff. Sampling is quite often used in our day-to-day practical life. For example, in a shop we assess the quality of sugar, wheat or any other commodity by taking a handful of it from the bag and then decided to Sample Survey Unit 5
210 A Textbook of Probability and Statistics for BCA purchase it or not. A house wife normally tests the cooked products to find if they are properly cooked and contain the proper quantity of salt. i) Sampling frame: A complete list of the sampling units, which represents the population to be covered is called the sampling frame popularly known as frame. In other words, a list of all the elements that is in the population. ii) Sampling units: The sampling unit is the basic unit containing the elements of the population to be sampled. It may be the element itself or a unit in which the element is contained. The sampling unit selected is often dependent upon the sampling frame. The selection of sampling units is also partially dependent upon the overall design of the project. iii) Sample: A part or portion of the population which is considered for study and analysis is called a sample. In other words, a finite subset of the population with the objective of investigating its properties is called a sample and the number of units in the sample is known as the sample size. 5.2 Needs of Sampling Sampling is carried out because of following reasons i) Sampling saves time and money. Sample study is less expensive than census and gives faster result. ii) Only if test involves the destruction of items under investigation. Sample study prevents the items from destruction if items are of destructive nature. iii) Only way for the infinite population. For the infinite population complete enumeration is not possible so that sample method is only the method of collecting information. iv) Enable to estimate sampling error. The sample estimate gives the error from the population. v) Enable more accurate result. Sampling conducted by well trained and experienced investigator gives accurate result. 5.3 Census and Sample Survey Survey is the technique of investigation by direct observation of a phenomenon of collection of information through interview. The meaning of survey has been used in broader sense to include the observation of published documents. The survey is used describing current practice and events and analyzing the facts. The main objective of the survey are as follows: i) Supply of information on any problem ii) Description of the phenomenon iii) Explanation of a phenomenon Census The method of enumerating each and every unit of the population is known as census. Some of the examples are Population census, manufacturing census, agricultural sample census etc. Sample survey The survey carried out by selecting representative sample of the study population is known as sample survey. For example, Nepal living standard survey, family planning survey etc.
Sample Survey 211 5.4 Basic Concept of Sampling Generally, sampling has been employing not only in any statistical investigation and research works but also in the case of daily life of human beings. For example, i) A housewife tests very small quantity of cooking foods to know about the taste of whole food that she is cooking. ii) A doctor tests a drop of blood of a patient to know about the characteristic of the whole blood of the patient. iii) A businessperson gives order for the commodities by examining a small unit of the same commodity. In such practical decision making process associated with various fields of human activities, most of our conclusions, decisions, and findings depend upon the inspections or test or examination of few units of an aggregate or totality. This process of getting result or information of conclusion about the totality or universe or whole group by performing examination of only some parts of the universe under the study (investigation) is called sampling. In other words, sampling is the process by which inference is made to the whole by examining only a few parts. Sampling is a tool which enables us to draw conclusion about the characteristics of the population after studying the items in the sample. 5.5 Census versus Sampling A census is a study of every unit, everyone or everything, in a population. That is, a census is the complete enumeration or count of all units of the population for certain character of the population. Hence, the complete enumeration of all units of the population is known as Census Survey. The term census is used mostly in connection with National population census and Housing Censuses and other common censuses include agriculture census, business census, Industrial census survey etc. Census requires more money, manpower and time. The method or process of selecting a sample from a population under study is called sampling. A sample is a subset of units in a population selected to represent all units in a population. It is a partial enumeration because it is a count from part of the population. Therefore, the process (or survey) in which only part of the population is selected and examined to estimate the certain character of the population is known as sample survey. That is, the enumeration of the selected units is known as sample survey. Information from the sampled units is used to estimate the characteristics for the entire population. A sample survey will usually be less expensive than a census survey and the desired information will be obtained in less time. When and Where Sampling/Census is Appropriate: A sampling technique is appropriate a. When the universe is very large b. When the universe possesses homogeneous characteristics c. When utmost accuracy is not required d. Where census is impossible i.e., in destructive/explosive nature of testing. A census is appropriate when a. The universe is small b. The population is heterogeneous c. Hundred percent accuracy is required d. The population frame is incomplete
212 A Textbook of Probability and Statistics for BCA Demerits of Sampling Technique: i) Less accuracy ii) Misleading conclusions iii) Need of specialized knowledge iv) When sampling is not possible v) It cannot be used if the information of each and every unit of the population is required. Demerits of Census: i) Expensiveness ii) Excessive time and effort iii) Not applicable for destructive testing iv) For infinite population, it is not possible. 5.6 Distinction between Census and Sampling Census Sampling 1. It takes each and every unit of the population. 1. It takes representative part of the population. 2. It is costly and time consuming i.e., It requires more money, manpower and time. 2. It is less expensive and less time consuming, i.e., It requires less money, manpower and time. 3. It is more accurate. 3. It is less accurate. 4. It has less scope. 4. It has greater scope. 5. It is appropriate when the universe is small. 5. It is appropriate when the universe is large. 6. It is appropriate when the population is heterogeneous. 6. It is appropriate when the universe possess homogeneous characteristics. 5.7 Organizational Aspect Sampling Survey 5.7.1 The Basic Organization Aspect Sampling Survey i) Objective of the Survey The first step in sampling is to define the objective of the survey in clear & lucid term. The sponsor of the survey should take care that these objectives are commensurate with the available resources in terms of money, manpower and the time limit required for availability of the results of the survey. ii) Defining Population to be Sampled The population i.e., the aggregate of objects from which sample is chosen should be defined in a clear and unambiguous terms. The population to be sampled (the sampled population) should be coincided with the population about which information is wanted (The target population). The definition of the population when sampling a batch of electric light bulb in order to estimate the average length of life of a bulb is clear but in sampling a population of farms, rules must be setup to define a farm regarding shape, size etc. keeping in mind the boarder-line cases so as to enable the investigator to decide in the field without much hesitation whether or not to include a given farm in the population. iii) Data to be collected It is well to verify that all the data are relevant to the purpose of the survey and that no essential data are omitted. There is frequently a tendency, particularly with human population to ask too many questions, some of which are never subsequently analyzed. An overlong questionnaire lowers the quality of the answer to important as well as unimportant questions.