Mathematical Theory and Modeling www.iiste.org ISSN 2224-5804 (Paper) ISSN 2225-0522 (Online) Vol.4, No.6, 2014 102 On the Selection of Samples in Probability Proportional to Size Sampling: Cumulative Relative Frequency Method Faruq Abdulla Student, Department of Statistics, Islamic University, Kushtia-7003, Bangladesh, Email: faruqiustat09mnil@gmail.com Md. Moyazem Hossain (Corresponding author) Department of Statistics, Islamic University, Kushtia-7003, Bangladesh, E-mail: mmhrs.iustat@gmail.com Md. Mahabubur Rahman Department of Statistics, Islamic University, Kushtia-7003, Bangladesh, E-mail: sagorju151@gmail.com Abstract Generally in the sense that, the unit with large size contain more ancillary information than the unit with smaller size. So when samples from different sized subgroups or units are used and sampling is taken with the same probability, the chances of selecting a member from a large group are less than selecting a member from a smaller group although here the chances of selecting a member from a large group will be greater than selecting a member from a smaller group. That is it is clear that, the probability of selecting a unit is positively proportional to its size. The aim of this paper is to propose a method of selecting samples in probability proportional to size. This method uses relative frequency to select samples in probability proportional to size. Comparatively it takes less time and easy to apply than Cumulative Total Method and Lahiri’s Metho d. Keywords: Probability Proportional to Size (PPS) Sampling, Cumulative Total Method, Lahiri’s Method, Cumulative Relative Frequency Method. 1. Introduction Sampling is a research method where subgroups or units are selected from a larger group known as a target population. The subgroups or samples are studied. If the sample is correctly chosen then the results can be used to represent the target population. In almost all practical situations the size of the sampling units whose are included in the sampling frame are vary from one to another. Generally in the sense that, the unit with large size contain more ancillary information than the unit with smaller size. So when samples from different sized subgroups or units are used and sampling is taken with the same probability, the chances of selecting a member from a large group are less than selecting a member from a smaller group although here the chances of selecting a member from a large group will be greater than selecting a member from a smaller group. That is it is clear that, the probability of selecting a unit is positively proportional to its size. This is known as Probability Proportional to Size (PPS) sampling. If the selected unit with associated size in the sample is reconsidered in the sampling frame then it is known as PPS sampling with replacement but if the selected unit with associated size in the sample is ignored from the sampling frame then it is known as PPS sampling without sampling. There exist numerous methods for selecting a fixed size sample with probability proportional to size (PPS), with replacement. Traditionally, Simple Random Sampling (SRS) has been regarded as the method-of-choice because all elements in the population have an equal chance to get picked and hence, reducing selection bias and