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Lecture Notes : Statistics 2009 CHAPTER 1: INTRODUCTION 1 DEFINITION, NATURES AND IMPORTANCE OF STATISTICS The word statistics is derived from the Latin word status meaning “state”. Early uses of statistics involved compilation of data and graphs describing various aspects of the state or country. T...

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Lecture Notes : Statistics

2009

CHAPTER 1:

INTRODUCTION 1.1 DEFINITION, NATURES AND IMPORTANCE OF STATISTICS The word statistics is derived from the Latin word status meaning “state”. Early uses of statistics involved compilation of data and graphs describing various aspects of the state or country. The word statistics has two basic meanings. We sometimes use this word when referring to actual numbers derived from data and the other refers to statistics as a method of analysis. DEFINITION: Statistics a collection of quantitative data, such as statistics of crimes, statistics on enrollment, statistics on unemployment, and the like. Statistics is also a science, which deals with the collection, presentation analysis, and interpretation of quantitative data. Statistics involves much more than the simple collection, tabulation and summarizing of data. Statistics is also a tool that helps us develop general and meaningful conclusions that go beyond the original data. The following are some examples of the uses of statistics: Surveys Consumer Preference Experiments Sampling Economics NATURES OF STATISTICS DESCRIPTIVE STATISTICS It deals with the methods of organizing, summarizing and presenting a mass of data so as to yield meaningful information. INFERENTIAL STATISTICS It deals with making generalizations about a body of data where only a part of it is examined. This comprises methods concerned with the analysis of a subset of data leading to predictions or inferences about the entire set of data. Example: Determine whether the following statements use the area of descriptive statistics or statistical inference. 1. A bowler wants to find his bowling average for the past 12 games. 2. A manager would like to predict based on previous years’ sales, the sales performance of a company for the next five years.

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3. A politician would like to estimate, based on an opinion poll, his chance for winning in the upcoming senatorial election. 4. A teacher wishes to determine the percentage of students who passed the examination. 5. A student wishes to determine the average monthly expenditures on school supplies for the past five months. 6. A basketball player wants to estimate his chance of winning the most valuable player (MVP) award based on his current season averages and the averages of his opponents. Answer: 1. 2. 3. 4. 5. 6.

___________________ ___________________ ___________________ ___________________ ___________________ ___________________

Exercise 1.1 Direction: Classify the following statements as belonging to the area of descriptive statistics or statistical inference. Write DS for descriptive statistics and write IS for inferential statistics on the space provided. _________________1. Yesterday’s records show that five (5) employees were absent due to Dengue fever. _________________2. If the present trend continues, architects will construct more contemporary homes than colonials in the next 5 years. _________________3. In a certain city, arsonists deliberately set 3% of all fires reported last year. _________________4. At least 30% of all new homes being built today are of a contemporary design. _________________5. As a result of a recent poll, most Filipinos are in favor of finding work employment abroad. _________________6. Philippines’ Gross Domestic Product (GDP) grows by 4.6% in 2002, 1.4 percentage higher than its 3.2% performance in 2001. _________________7. The average grade of 10 students in English is 89.46%. _________________8. Based from the present sales trend, it is expected that after two years, this year’s sales will be doubled.

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_________________9. All four provinces of ARMM are among the 10 poorest provinces in the Philippines for 2002. _________________10. During the period 1996 to 2002, unemployment rates among women were consistently higher compared to men except in 1999 and 2000. 1.2 DEFINITION OF SOME BASIC STATISTICAL TERMS The following are terms commonly used in Statistics: 1. Population is the set of all individuals or entities under consideration or study. It may be a finite or infinite collection of objects, events, or individuals, with specified class or characteristics under consideration. Example 1. The researcher would like to determine the average age of patients infected with dengue fever for the month of June at Medical Center Imus. Population: the set of all patients with dengue fever. Example 2. The researcher would like to determine the number of BM students in CvSU-CBE. Population: the set of all students in CvSU-CBE. 2. Variable is a characteristic of interest measurable on each and every individual in the population, denoted by any capital letter in the English alphabet. Types of Variable Qualitative Variable consists of categories or attributes, which have non-numerical characteristics. Example: classification, year level, sex and subjects enrolled Quantitative Variable consists of numbers representing counts or measurements. Variable for population 1: A = age Variable for population 2: S = sex

3. 4. 5. 6.

Classification of Quantitative Variable Discrete Quantitative Variable results from either a finite number of possible values or a countable number of possible values. Example: number of students, number of books, and number of patients Continuous Quantitative Variable results from infinitely many possible values that can be associated with points on a continuous scale in such a way that there are no gaps or interruptions. Example: height, weight, grade point average, and time Sample is part of the population or a sub-collection of elements drawn from a population. Parameter is a numerical measurement describing some characteristic of a population. Statistic is a numerical measurement describing some characteristic of a sample. Survey is often conducted to gather opinions or feedbacks about a variety of topics.

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Census Survey, most often simply referred to as census, is conducted by gathering information from the entire population. Sampling Survey, most often simply referred to as survey, is conducted by gathering information only from part of the population.

Exercise 1.2.1 Direction: Identify the population, variable of interest, and type of variable in the following: 1. The dean of CIH would like to determine the average weekly allowance of BS HRM students. Population:______________________________________________________________ Variable: _______________________________________________________________ Type of variable:_________________________________________________________ 2. The registrar of DLSU-D would like to conduct a survey on the preferred courses of 4th year high school students in Cavite. Population:______________________________________________________________ Variable: _______________________________________________________________ Type of variable:_________________________________________________________ 3. The dean of the CBA would like to know the number of students who are smoking. Population:______________________________________________________________ Variable: _______________________________________________________________ Type of variable:_________________________________________________________ 4. A survey by a group of students entitled “Dress Code” will be conducted to first year students to determine the fashion preferences of these students. Population:______________________________________________________________ Variable: _______________________________________________________________ Type of variable:_________________________________________________________ 5. Information will be collected to new voters for 2004 election to identify their opinion regarding politics in the Philippines. Population:______________________________________________________________ Variable: _______________________________________________________________ Type of variable:_________________________________________________________

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6. From all students registered this semester, the Mathematics Department would like to know how many students like mathematics. Population:______________________________________________________________ Variable: _______________________________________________________________ Type of variable:_________________________________________________________ 7. A study to be conducted by NGO would determine the Filipinos’ awareness about the war against IRAQ. Population:______________________________________________________________ Variable: _______________________________________________________________ Type of variable:_________________________________________________________ 8. A group of students taking Statistics conducted a study on the effect of boy-girl relationship to the academic performance of the students. Population:______________________________________________________________ Variable: _______________________________________________________________ Type of variable:_________________________________________________________ 9. Some parents would like to determine whether Counter Strike is good or bad to the behavior of their children. Population:______________________________________________________________ Variable: _______________________________________________________________ Type of variable:_________________________________________________________ 10. The head librarian would like to identify the book/s commonly read by DLSU-D students. Population:______________________________________________________________ Variable: _______________________________________________________________ Type of variable:_________________________________________________________ 11. A statistics teacher, Ms. Nacion, would like to determine whether the number of students in a class at the start of the semester can determine the number of failures. Population:______________________________________________________________ Variable: _______________________________________________________________ Type of variable:_________________________________________________________

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Exercise 1.2.2 Direction: Identify each statement as having discrete or continuous data. Write D for discrete and C for continuous. _____________1. Among the 1,500,000 microcomputer chips made by Motocolla, 2 are found to be defective. _____________2. Yesterday’s records show that 25 students were absent. _____________3. Radar on EDSA indicated that the driver was going 150 kph when ticketed for speeding. _____________4. The amount of time that a taxi driver spends yielding to individual pedestrians each year is 2.367 seconds. _____________5. Upon completion of a diet and exercise program, Elmer weighed 12.37 lbs. less than when he started the program. Exercise 1.2.3 Direction: Identify which of the following quantitative data would be presented by a discrete variable or a continuous variable. Write DV for discrete variable and write CV for continuous variable. _____________1. Number of students _____________2. Time (in minutes) to finish an exam _____________3. Distance (in km.) of school from place of residence _____________4. Length (in cm) of fish caught _____________5. Width of the newest brand of cellular phone _____________6. Percentage increase in enrolment this year _____________7. Number of enrollees _____________8. Monthly income of 100 randomly selected persons at KADIWA Market _____________9. Sum of points in tossing a pair of dice _____________10. Lifetime (in years) of televisions produced by ZONY

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1.3 LEVELS OF MEASUREMENT Another common way to classify data is to use four levels of measurement. The level of measurement of data determines the algebraic operations that can be performed and the statistical tools that can be applied to the data set. The following are the four levels: Level 1. Nominal is characterized by data that consist of names, labels, or categories only. The data cannot be arranged in an ordering scheme. Examples: name, religion, civil status, address, sex, degree program Level 2. Ordinal involves data that may be arranged in some order, but differences between data values either cannot be determined or are meaningless. Examples: military rank, job position, year level Level 3. Interval is like the ordinal level, with the additional property that meaningful amounts of differences between data can be determined. However, there is no inherent (natural) zero starting point. Examples: IQ Score, temperature (in ⁰C) Level 4. Ratio is the interval level modified to include the inherent zero starting point. For values at this level, differences and ratios are meaningful. Examples: height, area, width, weekly allowance Exercise 1.3 At what level are the following variables measured? Write nominal, ordinal, interval or ratio on the space provided. ___________________1. Student number ___________________2. Weights of a sample of candies ___________________3. Zip codes ___________________4. SSS number ___________________5. Final course grades of 1.0,1.25,1.50,…. ____________________6. Instructors rated as superior, above average, average, below average, or poor ____________________7. Movies listed according to their genre such as, comedy, adventure, romance, action, suspense, or horror

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___________________8. Lengths of TV commercials ( in seconds) ___________________9. The years 1896, 2000, 1776,1995 ___________________10.Attitude toward gun laws such as favorable, somewhat favorable, somewhat unfavorable.. ___________________11.Exam score ___________________12. Ideal number of children ___________________13. Family Income ___________________14. Candidate voted for in 2002 barangay elections ___________________15. Tax Identification Number ___________________16. Gender ___________________17. Average number of glasses of water consumed per day ___________________18. Blood pressure ___________________19. Height of students ___________________20. Number of clients ___________________21. Number of won cases in court ___________________22. Academic rank in High School ___________________23. Savings Account Number ___________________24. Are you a Pag-Ibig Member?(Yes/No) ___________________25. Number of books sold per day ___________________26. Weekly allowance of CvSU-CBE ___________________27. Main source of income ___________________28. Birth order in the family ___________________29. Number of organizations involved in ___________________30. Car plate number

CHAPTER 2:

DATA COLLECTION AND PRESENTATION 2.1 METHODS OF DATA COLLECTION In order to have accurate data, the researcher must know the right sources and the right way of collecting them. CHARACTERISTICS OF A GOOD QUESTION 1. A good question is unbiased. Questions must not be worded in a manner that will influence the respondent to answer in a certain way that is to favor a certain response or to be against it. An unbiased question is stated in neutral language and no element of pressure. Examples of unbiased questions:

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a. Do you favor the enrollment procedure employed last semester? b. Do you like classical music? Examples of biased questions: a. Do you favor the enrollment procedure employed last semester which makes long lines shorter? b. Do you listen to boring classical music? 2. A question must be clear and simply stated. A question that is simple and clear will be easier to understand and more likely to be answered truthfully. Example of a simple and clear question: a. What is your average grade last semester?

Example of a not simple question: a. What is your academic performance last semester?

3. Questions must be precise. Questions must not be vague. The question should indicate clearly the manner how the answers must be given. Example of a precise question: a. In terms of mathematical ability, do you think male and female are equal? Example of a vague question: a. Do you think male and female are equal? 4. Good questionnaires lend themselves to easy analyses. TWO CATEGORIES OF SURVEY QUESTIONS 1. Open question- allows free response. Example: What do you think can be done to reduce crime? 2. Closed question- allows only a fixed response. Example: Which of the following approaches would be the most effective in reducing crime? Choose one. A. Get parents to discipline more.

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Correct social and economic conditions in slums. Improve rehabilitation efforts in jails. Give convicted criminals tougher sentences. Reform courts.

TYPES OF DATA 1. Primary Data- are information collected from an original source of data, which is first-hand in nature. Examples are data collected from interviews and surveys. 2. Secondary Data- are information collected from published or unpublished sources like books, newspapers, and thesis. FOUR IMPORTANT POINTS TO CONSIDER WHEN COLLECTING DATA 1. If measurements of some characteristics from people (such as height) are being obtained, better results will be achieved if the researcher does the measuring instead of asking the respondent for the value. 2. The method of data collection used may expedite or delay the process. Avoid a medium that would produce low response rates. 3. Ensure that the sample size is large enough for the required purposes. 4. Ensure that the method used to collect data actually results in a sample that is representative of the population. METHODS OF DATA COLLECTION 1. Direct or Interview Method The direct or interview method of data collection use at least two persons (an interviewer and interviewee/s) exchanging information. This method will give us precise and consistent information because clarifications can be made. Also, questions not fully understood by the respondent, the interviewer could repeat the question until it suits the interviewee’s level. However, this method is time consuming, expensive and has limited field coverage. 2. Indirect or Questionnaire Method This is a method where written answers are given to prepared questions. This method requires less time and is inexpensive since the questionnaires can be mailed or hand-carrried. Also, this will give a respondent a sense of freedom in honestly answering the questions because of anonymity. 3. Registration Method This is a method enforced by certain laws. 4. Observation Method This is a method, which observes the behavior of individuals or organizations in the study. This is also used when the respondents cannot read nor write. 5. Experiment Method This method is used when the objective of the study is to determine the cause and effect of certain phenomena or event.

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Exercise 2.1 A. Answer the following questions: 1. What are the advantages and disadvantages of open questions? 2. What are the advantages and disadvantages of closed questions? 3. Choose the letter that corresponds to an unbiased option. A. Anyone is free to smoke cigarettes if he wants to. __________ Agree _________Disagree B. No sane person will burn money on cigarettes. __________ Agree _________Disagree C. Smoking may be dangerous to your health. __________ Agree _________Disagree 4. Change the following questions to make it simpler and clearer. A. What is your opinion about beauty contest being demeaning to womanhood and against the vaunted equality of the sexes? B. What is your mass measure in metric units? 5. Determine which of the following questions is best to ask about someone’s health? A. Are you a weakling? B. Are you bursting over with health? C. Can you be an advertisement for a health club? D. Are you in good health? 6. To find out how much someone likes music, which ques...