Elementary Statistics and Probability Lesson 1 PDF

ELEMENTARY STATISTICS AND PROBABILITY LESSON 1  THE NATURE OF STATISTICS LEARNING OUTCOMES: a. discuss the contributions of the different statisticians/mathematicians in the continuous improvement of statistical knowledge and concepts b. differentiate between 1.Des...

ELEMENTARY STATISTICS AND PROBABILITY LESSON 1  THE NATURE OF STATISTICS LEARNING OUTCOMES: a. discuss the contributions of the different statisticians/mathematicians in the continuous improvement of statistical knowledge and concepts b. differentiate between 1.Descriptive and 2.Inferential Statistics 3.Population and Sample  STATISTICS Statistics, as popularly known, refer to numerical observations of almost any kind or any set of quantitative data, as in "vital statistics", or as used in the phrase "statistics shows…"  STATISTICS Statistics is a branch of science that deals with the collection, tabulation, or presentation, analysis, and interpretation of numerical or quantitative data.  Historically, The modern science of statistics traces its origins from two diverse interests of man:  POLITICS In political states ENTERTAINMENT In games of chances  Statistics Was described as the study of the political arrangements of the modern states of the known world.  Statistics Was derived from the world statista meaning statesman (one who is well-versed with public affairs).  ACHENWALL (1749) First used the word statistics, defining it as “the political science of several countries."  In the early 16 th century, Games of chances gave rise to the development of the principles of probability. Problems on how to increase their chances of winning were posed by gamblers who called upon mathematicians to provide them with optimum strategies for playing various games of chances. The answers given by mathematicians such as PASCAL, FERMAT, LEIBNITZ, CARDANO, BERNOULLI, and others became the basis of modern statistical theory. These represented the beginnings of the mathematics of probability.  During the 19th century, Applied statistical methods in the fields of education and sociology, and Known demonstrated as the ADOLF QUETELET that statistical Father of techniques Modern derived in one Statistics area of research are also applicable in other areas. Two Fields of Statistics: DESCRIPTIVE INFERENTIAL STATISTICS STATISTICS  Concerned with gathering, classification and presentation of data and the collection of values to describe group characteristics DESCRIPTIVE of the given data. STATISTICS Examples: Measures of central tendency, variability, skewness, kurtosis, etc.  Aims to give information about large groups of data (population) without dealing with each and every elements of these groups. It only uses a small but representative portion (sample) of the total set of data in order to draw INFERENTIAL conclusions or judgements regarding the STATISTICS entire set of data. Examples: Sampling/Sampling distribution, estimation, and testing of hypotheses using z-test, t- test, chi-square test, F-test, ANOVA, among others.  A population is the entire group that you want to draw conclusions about. POPULATION It can mean a group containing elements of anything you want to study, such as objects, events, organizations, countries, species, organisms, etc.  A sample is the specific group that you will collect data from. SAMPLE The size of the sample is always less than the total size of the population. POPULATION Advertisements for IT jobs in the Netherlands SAMPLE The top 50 search results for advertisements for IT jobs in the Netherlands on May 1, 2020 POPULATION Songs from the Eurovision Song Contest SAMPLE Winning songs from the Eurovision Song Contest that were performed in English CAN YOU SEE THE DIFFERENCE? ? Undergraduate students of BSU Bokod Campus ? 200 undergraduate students from the 3 colleges of BSU-Bokod who volunteered in the research study ? Countries with published data available on birth rates and GDP since 2000 ? All countries of the world  END OF LESSON 1  TYPES OF DATA & VARIABLES & MEASUREMENT LEARNING OUTCOMES: a. Identify the types of data and the level of measurement for each variable  TYPES OF DATA Classifications of data may vary. Data may be classified as raw, grouped, ungrouped, primary and secondary. RAW DATA are in their original form and structure. GROUPED DATA are placed in tabular form characterized by class intervals with the corresponding frequency. PRIMARY DATA are measured and gathered by the researcher that published it. SECONDARY DATA are published by another researcher or agency.  VARIABLES AND MEASUREMENT VARIABLE. A character or attribute of persons or objects, which assumes different values (numerical) or labels (quantitative) MEASUREMENT. The process of assigning the value or label of a particular experiment unit EXPERIMENTAL UNIT. The person or the object by which the variable is measured. CLASSIFICATION OF VARIABLES CLASSIFICATION OF VARIABLES EXAMPLES: Yields ✓ Civil Status categorical or (single, Married, qualitative Widow, etc.) responses. It refers to the ✓ Religious attributes on Affiliation characteristics (Roman Catholic, of the samples Protestant, etc.) CLASSIFICATION OF VARIABLES EXAMPLES: Yield numerical ✓ Height responses ✓ Weight representing ✓ Number of an amount children ✓ Age or quantity Discrete Quantitative Variables Continuous Quantitative Variables Discrete Quantitative Variables Assume finite or countable infinite values such as 0, 1, 2, 3, 4, … Examples: ✓Number of Children (0, 1, 2, 3,…) ✓Number of student-dropouts (2, 3, 4) CONTINUOUS Quantitative Variables Cannot take on finite values but the values are related/associated with points on an interval of the real line. Examples: ✓Height (5’4’’; 157cm; 1.5 m) ✓Weight (130.50 kilos; 210 lbs; 432 grams) ✓Temperature (32.5ᵒC; 112ᵒF)  LEVELS OF MEASUREMENT NOMINAL ORDINAL INTERNAL RATIO LEVEL LEVEL LEVEL LEVEL  LEVELS OF MEASUREMENT The crudest form of measurement. The numbers of symbols are used for the purpose of categorizing forms into groups. The NOMINAL categories are mutually exclusive, that is, being in one category automatically excludes another LEVEL EXAMPLES: Sex: M-Male , F- Female Faculty Tenure: 1- Tenured, 0- Non-tenured  LEVELS OF MEASUREMENT A sort of improvement of nominal level. Data are ranked from bottom to top or low to high manner. Statements of the kind greater than or ORDINAL less than may be made here LEVEL EXAMPLES: Class Standing (Excellent, good, poor) Teacher’s Evaluation (1-poor, 2-fair, 3-good, 4- very good)  LEVELS OF MEASUREMENT Possesses the properties of the nominal and ordinal levels. The distances between any two numbers on the scale are known and it does not INTERVAL have a stable starting point (an absolute zero) EXAMPLES: LEVEL Consider the IQ scores of four students 90, 150, 85 and 145. Here we can say that the difference between 90 and 150 is the same as the difference between 85 and 145 but cannot claim that the second student is twice as intelligent as the first.  LEVELS OF MEASUREMENT Possesses all the properties of the nominal, ordinal and interval levels. In addition, this has an absolute zero point. Data can be classified RATIO and placed in a proper order. We can compare the magnitudes of these data. LEVEL EXAMPLES: Age, income, exam scores, performance ratings, grades of students and tuition fees are examples of ration variables.  Summary Characteristics of the LEVEL OF MEASUREMENT LEVELS OF Classify Order Equal Limits Absolute Zero MEASUREMENT NOMINAL YES NO NO NO ORDINAL YES YES NO NO INTERVAL YES YES YES NO RATIO YES YES YES YES Here are 4 levels of measurement: Nominal: the data can only be categorized Ordinal: the data can be categorized and ranked Interval: the data can be categorized, ranked, and evenly spaced Ratio: the data can be categorized, ranked, evenly spaced, and has a natural zero. LET’S DO THIS! Classify the types of data whether NOMINAL, ORDINAL,INTERVAL, OR RATIO 1. Ethnicity 1.NOMINAL 2. Car brands 2.NOMINAL 3. Top 5 Olympic medalists 3.ORDINAL 4. Language ability (e.g., beginner, intermediate, fluent) 4.ORDINAL 5. Likert-type questions (e.g., very dissatisfied to very 5.ORDINAL satisfied) 6. Province of birth 6.NOMINAL 7. Test scores (e.g., IQ or exams) 7.NOMINAL 8. Personality inventories 8.INTERVAL 9. Temperature in Fahrenheit or Celsius 9.INTERVAL 10. Gender 10.INTERVAL YOUR TURN! Classify the types of data whether NOMINAL, ORDINAL,INTERVAL, OR RATIO 1. Color 2. Height 3. Class rankings 4. Age 5. survey responses 6. Weight 7. calendar dates 8. Temperature in Kelvin 9. Types of animals