Elective 8 Statistics Quarter 1.pdf

STATISTICS and PROBABILITY Stephanie Joy E. Lungub Teacher NCICTELOOL NIZTAAOOGIR ASNYSAIL TPIANIOERTR TNE STCIISSATT AADT VTPEDIISRCE ATLRIIFEENN QTEUIVAITTN A QLEVAITTIUA STATISTICS and PROBABILITY Stephanie Joy E. Lungub Teacher CONTE...

STATISTICS and PROBABILITY Stephanie Joy E. Lungub Teacher NCICTELOOL NIZTAAOOGIR ASNYSAIL TPIANIOERTR TNE STCIISSATT AADT VTPEDIISRCE ATLRIIFEENN QTEUIVAITTN A QLEVAITTIUA STATISTICS and PROBABILITY Stephanie Joy E. Lungub Teacher CONTENTS First Quarter Statistical Terminologies Collection of Data Graphical Presentation of Data Tabular Presentation of Data  tatistical erminologies  The learner will be able to: 1. explain the importance of Statistics. 2. pose problems that can be solved using Statistics; and LEARNING 3. formulate simple statistical COMPETENCIES instruments.  What is STATISTICS? Statistics is 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. TYPES OF DATA Collection of data Organization of data Analysis of data Interpretation of Data COLLECTION OF DATA refers to the process of obtaining information. ORGANIZATION OF DATA refers to the ascertaining manner of presenting the data into tables, graphs, or charts so that logical and statistica; conclusions can be drawn from the collected measurements. ANALYSIS OF DATA to the process of extracting relevant information from the given data from which numerical description can be formulated. INTERPRETATION OF DATA refers to the task of drawing conclusions from the analyzed data. TWO MAJOR AREAS OF STATISTICS Descriptive Statistics Inferential Statistics What is the difference of descriptive and inferential statistics? DESCRIPTIVE STATISTICS is a statistical method concerned with describing the properties and characteristics of a set of data. For intance, respondents in a survey may be described in terms of how many are males and how many are females, what percent are literate, what is the average family income, how many belong to a certain age group, etc. Descriptive Statistics involves data gathering, organizing, describing, and presenting information. INFERENTIAL STATISTICS is a statistical method concerned with the analysis of a sample data leading to prediction, inferences, interpretation, or conclusion about the entire population. For instance, suppose a survey group wants to know the prevailing sentiments among Filipino people on a certain issue. Asking every Filipino to answer a questionnaire would be impossible. It is expensive, time-consuming, and impractical. Instead, a small part of the entire population is scientifically chosen. The data gathered from this group is used to draw a general opinion of the entire population. Tell whether each situation will make use of descriptive or inferential statistics. 1. A sari-sari store owner records the frequency of sales of the five leading detergent soaps DESCRIPTIVE STATISTICS Recording of frequency of sales leads to describing the most popular brand Statistics Break Slide APPLICATION OF STATISTICS In modern times, applications of statistical methods in the social sciences began to increase. Statistics became essential in education, government, business, economics, medicine, psychology, sociology, sport, and others.  Education Statistical tools are used to get the information on the enrollment, finance, facilities, grading system, and so on.  Government Statistics are gathered to guide the officials in managing the affairs of the state. Since the earlier times, most civilized countries have already compiled large-scale statistics in order to ascertain the manpower and material strength of the nation. Intelligent Policy-Making and Administration Large amounts of concrete and organized records on the movement of population, taxes, cost of living, wages, and resources are necessary. Medicine and Physical Sciences The causes and effects of factors which affect experiments are best evaluated using different statistical techniques.  Psychologists Able to understand human behavior better if they are able to gather, systematize, analyze, and interpret data on different tests resulting to intelligence test scores, aptitudes, personality trait ratings, and attitudes.  Sociology Statistics used in the study of the conditions of the society. In order to improve a society, different observations must be done, and with proper analysis and interpretation, it may result to a positive action that will benefit the people.  Business and Economics Statistics plays an important role in the financial transactions and marketing of new products, forecasting of business trends, controlling of the quality of goods produced, and improving personnel relations. Policy changes and decisions for more efficient business and economic management must be based on collected data which had undergone scientific statistical studies.  Sports Statistics are taken and recorded. These records are used to keep track of succeeding performances for comparison. Also, sports officials use them to decide on the team composition for international competition, and the declaration of the best athletes in their respective fields.  SOME STATISTICAL TERMS Some statistical terms that are often used in the study of statistics are as follows: 1. Data is any quantitative or qualitative information. a. Quantitative data refers to numerical information obtained from counting or measuring that can be manipulated by any fundamental operation. Examples: age, IQ scores, height, weight, income b. Qualitative data refers to descriptive attributes that cannot be subjected to mathematical operations. Examples: gender, citizenship, educational attainment, religion 2. Population refers to the totality of all the elements or persons for which one has an interest at a particular time. For example, the members of the faculty of a school, the graduating class, the Visayan-speaking employess of a company, the male students, etc. A particular variable of a population can be associated to the population. A researcher may associate a population to the ages of graduating students, the IQ scores of the employees, the income of single parents, and so on. The usual notation for population is N. 3. Sample is a part of a population determined by sampling procedures. It is usually denoted by n. 4. Parameter is any statistical information or attribute taken from a population. It is a true value or actual statistics since its source is the population itself. 5. Statistic is any estimate of statistical attributes taken from a sample. 6. Variable is a specific factor, property, or characteristics of a population or a sample which differentiates a sample or group of samples from another group. For example, the scores obtained from a coeducation class may differ by gender. Hence, gender is considered variable. a. Discrete variable is a variable that can be obtained by counting. Examples: the number of cell phone users in a company, the number of computers in the laboratory a. Continuous variable is a variable that can be obtained by measuring objects or attributes. Example: weight of students, the area of the classroom, temperature in a city over the period of time SCALES OF MEASUREMENTS NOMINAL MEASUREMENT ORDINAL MEASUREMENT This type of statistical data This provides the degree of depicts the presence or absence the presence of an attribute. of a certain attribute. This usually Usually, data is classified involves the random assignment according to orders or ranks. of numbers to represent the Ex. academic ranking, degree attribute. Ex. race, color, of illness classification, gender, civil status SCALES OF MEASUREMENTS INTERVAL MEASUREMENT RATIO The measurement where data This measurement is an are arranged in some order and interval level modified to the differences between data are include the inherent zero meaningful. Data at this level starting point. may lack inherent zero starting Ex. physical quantities, point. Ex. temperature allowance Sigma Notation Write the following expression in sigma notation Write the following expression in sigma notation Write the following expression in sigma notation Expand Expand THEOREMS CONCERNING SUMMATION The summation notation is governed by a set of laws. These are stated in the following theorems: COLLECTION OF DATA DATA MAY BE GATHERED THROUGH THE FOLLOWING METHOD Interview Questionnaire Observation Registration Experimentation DATA MAY BE GATHERED THROUGH THE FOLLOWING METHOD Interview Questionnaire Observation Registration Experimentation The example suggests that as the margin of error is set at a smaller percentage, the number of samples get closer and closer to the number of population. Note that a certain degree of error is committed when samples are used instead of the entire population. After determining the number of samples, the next thing to do is to know how these samples are gathered and what factors are to be considered in getting these samples.  SAMPLING TECHNIQUES 1. Probability Sampling Random Sampling Systematic Sampling Stratified Random Sampling Cluster Sampling 2. Nonprobability Sampling Convenience Sampling Quota Sampling Purposive Sampling