MATH 4 1

• Statistics


  A branch of mathematics that deals with the scientific collection, organization, presentation, analysis and interpretation of numerical data in order to obtain useful and meaningful information
• Collection of data


  Obtaining/gathering information
• Organization of data


  Ascertaining manner of presenting the data into tables, graphs, or chart so that logical and statistical conclusions can be drawn from the collected measurements
• Analysis of data


  Extracting from the given data relevant information from which numerical description can be formulated
• Interpretation of data


  Drawing conclusion from the analyzed data
• Ancient times used statistics

  • Ancient Egypt used statistics to count the number of heads of families
  • Ancient Judea and the Romans used it to estimate population
• Census


  The process of determining the population
• Importance and Application of Statistics

  • In Business
  • In Education
  • In Psychology
  • In Politics and Government
  • In Medicine
  • In Agriculture
  • In entertainment
  • In Everyday Life
• Descriptive Statistics


  A statistical method concerned with describing the properties and characteristics of a group of persons, places, or thing
• Inferential Statistics


  A statistical method/procedure concerned with drawing inference or information about the properties or characteristics of a population by studying its representative sample
• Descriptive Statistics


  • Counting the number of various furniture inside the school
  • Calculating the average height of the buildings along the Taft Avenue
  • Computing the average grade of students and determining the top ten students
• Inferential Statistics


  • Testing the relative effectiveness of a new brand of medicine in curing pimples and other
  • Predicting future sales of a company based on the present sales
  • Investigating if there is a significant relationship between mental age and chronological age
• Population


  Refers to the large collection or totality of objects, persons, places, or things. Denoted by N.
• Dependent Variable


  • A variable which is affected or influenced by another variable.
• Summary


  • Population and Sample
  • Parameter and Statistic
  • Discrete Variable (counting) and Continuous Variable (measuring)
  • Quantitative Data (numerical) and Qualitative Data (categorical)
  • Primary and Secondary sources of Data
  • Dependent and Independent Variables
• Classify the following as quantitative (A) or qualitative (B) data
• Ways of Collecting Data

  • The Direct or Interview Method
  • The Indirect or Questionnaire Method
  • The Registration/Census Method
  • The Experimental Method
• The Direct or Interview Method


  • Researcher has a direct contact with the interviewee
  • The researcher obtains the information needed by asking questions and inquiries from the interviewee
  • It is costly and time-consuming
• Sampling Techniques


  Procedures used to determine the individuals or members of a sample
• Probability Sampling


  Sampling technique wherein each member or element of the population has an equal chance of being selected as members of the sample
• Non-Probability Sampling


  Members of the sample are drawn from the population based on the judgement of the researchers. This technique are not so reliable and the results of the study are relatively biased.
• Examples of Probability Sampling

  • Random Sampling
  • Systematic Sampling
  • Stratified Random Sampling
  • Cluster Sampling
  • Multi-Stage Sampling
• Random Sampling


  The basic type of probability sampling where each individual in the population has an equal chance of being drawn into the sample
• Random Sampling Techniques


  • Lottery Method
  • Table of Random Numbers
• Systematic Sampling


  There is a random starting point, then draw successive elements from the population
• Stratified Random Sampling


  Dividing the elements of a population into different categories and the members of the sample are drawn proportionally from each subpopulation
• Cluster Sampling


  When the population is so large, select or draw the members of the sample by group and then select a sample of elements from each cluster or group randomly
• Multi-Stage Sampling


  Usually used by researchers who are interested in studying a very large population
• Examples of Non-Probability Sampling

  • Convenience Sampling
  • Quota Sampling
  • Purposive Sampling
• Convenience Sampling


  Used only because of the convenience it offers to the researcher
• Quota Sampling


  Similar to stratified random sampling but the selection of the members of the sample is not done randomly
• Purposive Sampling


  The members of the sample are only chosen by the researchers based on their study
• Stratified Random Sampling Example

  1. Find the percentage of each stratum by dividing the number of families in each stratum by the total number of families

  2. Multiply each percentage by the desired number of families in the sample