CO1-L1- Introduction to Statistics and Probability PDF

MATH03 Statistics and Probability Course Outcome 1 Lesson 1: INTRODUCTION TO STATISTICS AND PROBABILITY shs.mapua.edu.ph Objectives At the end of the discussion, students must be able to: apply the basic concepts of Statistics to real...

MATH03 Statistics and Probability Course Outcome 1 Lesson 1: INTRODUCTION TO STATISTICS AND PROBABILITY shs.mapua.edu.ph Objectives At the end of the discussion, students must be able to: apply the basic concepts of Statistics to real world problems, compute appropriate sample size, differentiate parameter and sample, classify variables, illustrate a random variable (discrete and continuous), and distinguish between a discrete and a continuous random variable. shs.mapua.edu.ph  Definition Statistics is the science of collecting, analysing, presenting, and interpreting data, as well as of making decisions based on such analyses. Prem Mann, Introductory Statistics, 9/E Copyright © 2015 John Wiley & Sons. All rights reserved. shs.mapua.edu.ph  DEFINITION Statistics is a science that helps us make decisions and draw conclusions in the presence of variability. Retrieved from https://www.lifewire.com/how-to-use-facebook-reactions-3894307, Sept 7, 2021 shs.mapua.edu.ph Two Aspects of Statistics STATISTICS Theoretical/ Applied Mathematical Statistics Statistics shs.mapua.edu.ph Two Aspects of Statistics THEORETICAL MATHEMATICAL STATISTICS It deals with the development, derivation and proof of statistical theorems, formulas, rules and laws. shs.mapua.edu.ph Two Aspects of Statistics APPLIED STATISTICS It involves the applications of these theorems, formulas, rules and laws to solve real world problems shs.mapua.edu.ph TWO NATURE OF APLIED STATISTICS STATISTICS Theoretical/ Applied Mathematical Statistics Statistics Descriptive Inferential shs.mapua.edu.ph  Definition Descriptive Statistics consists of methods for organizing, displaying, and describing data by using tables, graphs, and summary measures. Prem Mann, Introductory Statistics, 9/E Copyright © 2015 John Wiley & Sons. All rights reserved. shs.mapua.edu.ph DESCRIPTIVE STATISTICS For example, suppose a pet shop sells cats, dogs, birds and fish. If 100 pets are sold, and 40 out of the 100 were dogs, then one description of the data on the pets sold would be that 40% were dogs. shs.mapua.edu.ph DESCRIPTIVE STATISTICS Some other measurements in descriptive statistics answer questions such as 'How widely dispersed is this data?', 'Are there a lot of different values?' or 'Are many of the values the same?', 'What value is in the middle of this data?', 'Where does a particular data value stand with respect with the other values in the data set?' shs.mapua.edu.ph EXAMPLES: A new supervisor in charge of 40 clerks would like to know their average salary. The market researcher of a manufacturing company constructs a graph showing the fluctuation in sales for a major product line during the last 3 years. As a result of a recent school survey, many students are not in favor of charter change. shs.mapua.edu.ph PHILIPPINE POPULATION BY REGION (2015) Data Source: Philippine Statistics Authority Official website (psa.gov.ph) Retrieved, June 11, 2021 shs.mapua.edu.ph  Definition Inferential Statistics consists of methods that use sample results to help make decisions or predictions about a population. shs.mapua.edu.ph INFERENTIAL STATISTICS Instead of using the entire population to gather the data, the statistician will collect a sample or samples from the millions of residents and make inferences about the entire population using the sample. shs.mapua.edu.ph EXAMPLES: A tire dealer wishes to estimate the average life of a particular brand of tire. A company projects a 50% growth in the next five years after analyzing its revenue for the past five years. shs.mapua.edu.ph POPULATION AND SAMPLE To collect data for any statistical study, a population must first be defined. Population indicates a group that has been designated for gathering data from. The data is information collected from the population. The sample is a set of data taken from the population to represent the population. shs.mapua.edu.ph POPULATION It consists of a complete set of individuals, objects, places, items, events or measurement of interest whose characteristics are being studied. The population that is being studied is called the target population. Retrieved from https://www.freepik.com/free-vector/fun-people-forming- circle_1311988.htm#page=1&query=population&position=2, Sept. 7, 2021 shs.mapua.edu.ph A population is not necessarily referring to people. A population could be a group of people, measurements of rainfall in a particular area or a batch of batteries. shs.mapua.edu.ph  POPULATION Finite Infinite shs.mapua.edu.ph EXAMPLES of FINITE POPULATION The children attending school in Butuan City. The prices of all mathematics books published in the Philippines during the past three years. Cards in a deck The percentage of all females who earns less than Php100, 000 a year. shs.mapua.edu.ph EXAMPLES of INFINITE POPULATION The possible rolls of a die The possible observations in any specific experiments. shs.mapua.edu.ph  SAMPLE - is a portion, or part of the population selected for study drawn by some appropriate methods from the population. shs.mapua.edu.ph  PARAMETER -value or measurement obtained from a population STATISTIC - value or measurement from a sample. shs.mapua.edu.ph  SURVEY Collection of information from the elements of a population or a sample. Census Sample survey survey that includes technique of collecting every element of the information from a target population portion of the population. shs.mapua.edu.ph Why do you take sample instead of studying every member of the population? It is not practical or feasible to use the entire population considering some factors. shs.mapua.edu.ph Determining the Sample Size Slovin’s Formula 𝑁 𝑆𝑎𝑚𝑝𝑙𝑒 𝑆𝑖𝑧𝑒 𝑛 = 1 + 𝑁𝑒 2 Where, 𝒏 = 𝒓𝒆𝒒𝒖𝒊𝒓𝒆𝒅 𝒔𝒂𝒎𝒑𝒍𝒆 𝒔𝒊𝒛𝒆 𝑵 = 𝒕𝒉𝒆 𝒔𝒊𝒛𝒆 𝒐𝒇 𝒕𝒉𝒆 𝒇𝒊𝒏𝒊𝒕𝒆 𝒑𝒐𝒑𝒖𝒍𝒂𝒕𝒊𝒐𝒏 𝒆 = 𝒎𝒂𝒓𝒈𝒊𝒏 𝒐𝒇 𝒆𝒓𝒓𝒐𝒓 shs.mapua.edu.ph  The problem that is commonly encountered is determining the sample size. It is not advisable to set a certain percentage; instead, the margin of error which is from 1% to 10% in social science researches should be considered. The margin of error is the error we expect to commit in getting the sample since it is an estimate of parameter. shs.mapua.edu.ph EXAMPLE: A group of researcher was tasked by the House of Representative to survey whether student in Metro Manila favor the moving of the start of classes from June to September. If there are 1, 000, 000 students and 10% margin of error are expected, compute the sample size. shs.mapua.edu.ph Given 𝑁 = 1, 000, 000 𝑁 𝑆𝑎𝑚𝑝𝑙𝑒 𝑆𝑖𝑧𝑒 𝑛 = 𝑒 = 10% 1 + 𝑁𝑒 2 1, 000, 000 𝑆𝑎𝑚𝑝𝑙𝑒 𝑆𝑖𝑧𝑒 𝑛 = 1 + 1, 000, 000 0. 10 2 1, 000, 000 𝑆𝑎𝑚𝑝𝑙𝑒 𝑆𝑖𝑧𝑒 𝑛 = 10, 001 𝑆𝑎𝑚𝑝𝑙𝑒 𝑆𝑖𝑧𝑒 𝑛 = 99. 9 𝑺𝒂𝒎𝒑𝒍𝒆 𝑺𝒊𝒛𝒆 𝒏 = 𝟏𝟎𝟎 shs.mapua.edu.ph EXAMPLE: Suppose that you have a group of 1,000 city government employees and you want to serve them to find out which tools are best suited in their jobs. You decide that you will use 0. 05 as a margin of error. Using Slovin’s formula, what is the required sample size? shs.mapua.edu.ph Given 𝑁 = 1, 000 𝑁 𝑆𝑎𝑚𝑝𝑙𝑒 𝑆𝑖𝑧𝑒 𝑛 = 𝑒 = 0. 05 1 + 𝑁𝑒 2 1, 000 𝑆𝑎𝑚𝑝𝑙𝑒 𝑆𝑖𝑧𝑒 𝑛 = 2 1 + 1, 000 0. 05 1, 000 𝑆𝑎𝑚𝑝𝑙𝑒 𝑆𝑖𝑧𝑒 𝑛 = 3.5 𝑆𝑎𝑚𝑝𝑙𝑒 𝑆𝑖𝑧𝑒 𝑛 = 285. 714 𝑺𝒂𝒎𝒑𝒍𝒆 𝑺𝒊𝒛𝒆 𝒏 = 𝟐𝟖𝟔 shs.mapua.edu.ph WHAT IS VARIABLE? It is an observable characteristics or attribute associated with the population or sample being studied which makes one different from the other. QUANTITATIVE OR QUALITATIVE shs.mapua.edu.ph QUANTITATIVE VARIABLE - Variables that are classified according to numerical value. EXAMPLES: age annual income weight market sales Price of cars test scores shs.mapua.edu.ph  QUANTITATIVE VARIABLE Discrete Continuous shs.mapua.edu.ph  Discrete Variable It can assume values only at specific points on a scale of values with gaps between them. A variable whose values are a result of counting. shs.mapua.edu.ph EXAMPLES: Number of days in a week Number of children in the family Number of students in the classroom Number of house and lots sold on a particular day Number of people visiting a bank Number of teachers in school shs.mapua.edu.ph  Continuous Variable A variable that can assume any numerical value over a certain continuous interval or it is a result of measurement. shs.mapua.edu.ph EXAMPLES: weight area height density volume temperature The time spent to serve a customer by a department store cashier. shs.mapua.edu.ph  QUALITATIVE VARIABLE - can be classified into two or more non-numeric categories according to its characteristics or attributes EXAMPLES: Civil status Color Nationality Zip Code shs.mapua.edu.ph  QUALITATIVE VARIABLE Dichotomous Multinomial shs.mapua.edu.ph  Dichotomous Variable It can be made only in two categories. EXAMPLES: Defective or Non-Defective Present or Absent Yes or No shs.mapua.edu.ph  Multinomial Variable Variable can be made in more than two categories EXAMPLES: Educational Attainment Nationality Brand of Soft drinks shs.mapua.edu.ph Types of Variables Variables Quantitative Qualitative Discrete Continuous Dichotomous Multinomial shs.mapua.edu.ph Sample Exercise Identify the following variables whether they are qualitative or quantitative. If it is quantitative, identify further if it is discrete or continuous. If it is qualitative, identify further if it is dichotomous or multinomial. 1. Highest Educational Attainment 2. Result of Tossing a Coin 3. No. of Students in a section 4. Civil Status 5. Amount Spent on Rice Last Week by the Household shs.mapua.edu.ph Sample Exercise: Answers Identify the following variables whether they are qualitative or quantitative. If it is quantitative, identify further if it is discrete or continuous. If it is qualitative, identify further if it is dichotomous or multinomial. 1. Highest Educational Attainment – Qualitative: Multinomial 2. Result of Tossing a Coin - Qualitative: Dichotomous 3. No. of Students in a section - Quantitative: Discrete 4. Civil Status - Qualitative: Multinomial 5. Amount Spent on Rice Last Week by the Household - Quantitative: Continuous shs.mapua.edu.ph Variables according to Levels of Measurement LEVELS OF MEASUREMENT Ratio Interval Ordinal Nominal shs.mapua.edu.ph NOMINAL It is a measurement scale that involves the process of naming or labeling the items by placing cases into categories and counting their frequency of occurrences. EXAMPLES: Gender Nationality Political Affiliation Car Dealers Civil Status Religion shs.mapua.edu.ph ORDINAL It is a measurement scale that yields information about the ordering of categories. EXAMPLES: Honor Roll Levels of Job performance Ranking of Faculty Members Evaluation of a product shs.mapua.edu.ph  INTERVAL It is a measurement scale that shows order of cases into categories considering and indicating the exact differences between and among the cases. EXAMPLES: Military Time Examinations Temperature Longitude & Latitude Retrieved from https://gfycat.com/heftysparsehalcyon, Sept. 7, 2021 shs.mapua.edu.ph RATIO It is a measurement that possesses all the characteristics of interval scale and for which the interval size and the ratio of two values have meanings. EXAMPLES: Measurements of weights, heights, lengths and ages shs.mapua.edu.ph Levels of Measurement Retrieved from https://conjointly.com/kb/levels-of- measurement/, Sept 7, 2021 shs.mapua.edu.ph LEVELS OF MEASUREMENT Level Property Basic Empirical Operation Nominal No order, distance and origin Determination of equivalence Ordinal Has order, but no distance or unique Determination of greater or origin lesser values Interval Both with order and distance but no Determination of equality of unique origin intervals or difference Ratio Has order, distance and unique origin Determination of equality of ratios or means shs.mapua.edu.ph Sample Exercise Identify the following variables according to their levels of measurement. 1. Highest Educational Attainment 2. Result of Tossing a Coin 3. No. of Students in a section 4. Civil Status 5. Amount Spent on Rice Last Week by the Household shs.mapua.edu.ph Sample Exercise: Answers Identify the following variables according to their levels of measurement. 1. Highest Educational Attainment 2. Hair Color 3. Temperature 4. Civil Status 5. Amount Spent on Rice Last Week by the Household shs.mapua.edu.ph Sample Exercise: Answers Identify the following variables according to their levels of measurement. 1. Highest Educational Attainment – Ordinal 2. Hair Color – Nominal 3. Temperature – Interval 4. Civil Status – Nominal 5. Amount Spent on Rice Last Week by the Household – Ratio shs.mapua.edu.ph shs.mapua.edu.ph