CHAPTER SIXTEEN

POPULATION OF STUDY

16.1 Objectives

At the end of this chapter, you should be able to:

        i.            explain the meaning of population.

      ii.            define sample; and

    iii.            discuss the sampling techniques

16.2 Introduction

In this chapter, you will learn the concepts of population and sample in relation to research study in mathematics education, since the two concepts are fundamental importance in any research. Also, the sampling procedure used in research will be adequacy defined and discuss in this chapter.

16.3 Concept of Population

Population is a set of components, events, objects, or all members of a well-defined class of individuals who share one or more traits of interest to researchers. For example, the total number of Mathematics students at Lafiagi College of Education. A population is also described as a collection of people who share at least one trait that differentiates them from other people (Creswell, 2012). The basic goal of research is to identify universally applicable principles, yet studying the entire population in order to reach generalizations would be impracticable, if not impossible. To address this size issue, a subset of the population must be selected for real investigation. This method of reducing a huge general population to a sample is typical in educational research (Best & Kahn, 2009).

16.4 Research Sample

Not often is it feasible for a researcher to examine the entire population. When this occurs, just a subset of the population is examined. Sample refers to the fraction of the population picked for the study. Therefore, a section of the population or universe is selected for research as a representative sample of the complete population or universe. Or, a sample is a subset of the population to whom the researcher aims to generalize his or her findings. Therefore, using a sample provides the following benefits:

§  It decreases costs

§  It saves time

§  It enables the execution of large-scale investigations

§  It increases precision

16.5 Sampling Technique

Sampling is the study of a group of individuals or observations from a larger set in order to derive conclusions about the characteristics of the larger population. According to Sambo (2008), the type of sampling technique utilized in research has a direct effect on the quality of conclusions drawn from the results of the study. There are several sampling procedures, including:

(4) Systematic Sampling

16.5.1 Simple Random Sampling

This is a method for picking a sample in which each member of the population or person has an equal and independent probability of being picked. For instance, if the chair of a college's mathematics department is tasked with selecting five 200-level students with a GPA of at least 4.0 for the COWBELL scholarship, the following criteria must be met: If there are twenty such students, the H.O.D. can assign numbers 1 through 20 to each student's name on separate pieces of paper. He can then fold these numbers, place them in a bag, thoroughly mix the papers, and ask someone to select a paper from the bag. The number and name can then be noticed and recorded. The paper was returned, and the procedure was repeated until five pupils emerged.

16.5.2 Stratified Random Sampling

It is sometimes preferable to partition the population into smaller homogenous groups in order to get a more precise representation. In the first step of this procedure, the total population is split or stratified into a number of relevant strata or groups. For instance, gender, locality, socioeconomic position, religious affiliation, years of education, or departments. Individuals are then chosen at random from each stratum or unit to constitute the sample. The numbers picked from each stratum may be proportionate or equal to the proportion of the population that falls into each stratum. There are two kinds of stratified random sampling: proportional and disproportionate (Teddlie & Yu, 2007). For instance: to pick 200 students from the N.C.E 2 students of the mathematics department at the College of Education in Minnesota. The strata can include combinations like Math/Economics, Math/Geography, Math/Physics, Math/Chemistry, and Math/Special Education. 3 Cluster or Area Sampling: is a sampling technique in which the unit of selection, known as the cluster, comprises two or more individuals of the population. Cluster sampling is effective when the individuals of a population are naturally clustered, for example. If there are ten schools, ten S.S.S. III pupils from Bosso Local Government will participate in an experiment. Here are the 10 schools in the group or unit. Consider that the researcher requires two schools, one for experimental and one for control purposes. Two schools might be selected at random to comprise his/her sample. Then allocate randomly one each to the experimental and control groups.

16.5.3 Systematic Sampling

This is a sampling procedure in which all the members of population (Sampling Units) are arranged alphabetically (or in some natural sequence or systematic fashion) and a sample is obtained by taking individuals at a fixed interval (K^th), K=  where “N” is the population size and “n” is the desire sample size. For example: if the HOD of mathematics is asked to select 5 students whose C.G.P.A is 4 points and above for an award. If there are 20 such students, he can assign numbers to all the students, and then randomly select one number. Assume that the first number selected is “3” then others will be selected at the interval of =4. Therefore, he will select Numbers: 3, 7, 11, 15, and 19 for the award

Student Activity

1.      Briefly explain the population

2.      Define the word sample

3.      Distinguish between population and sample

4.      List three merits of sample in research study

16.6 Summary

You now understand that the total population is the collection of people, things, events, and other things that share certain characteristics. The population's subset is known as the sample. Sampling allows for the creation of samples that are really representative of the target population. The process of selecting a sample from a target population is called sampling. These methods include basic random sampling.

References

Awotunde, P.O & Ugodulunwa (2002). An introduction to statistical methods in education Printed and Published in Nigeria by Fab Anieh (Nig) Ltd.

National Teachers’Institute, Kudana & National Open University of Nigeria, (2016). General education courses