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Lecture Notes : Statistics 2009 1 CHAPTER 1: INTRODUCTION At the end of this chapter, the students are expected to: a. Determine the nature of statistics applicable to a given situation; b. Identify population and variable in a given situation or problem; and, c. Classify the data according to variable type and appropriate level of measurement. 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. Lecture Notes : Statistics 2009 2 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. 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. ___________________ Lecture Notes : Statistics 2009 3 Name:_________________________________ Score:___________________ Course/Year/Section:_____________________ Teacher:_________________ 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. Yesterdays 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 years sales will be doubled. _________________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. Lecture Notes : Statistics 2009 4 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 BOM students at DLSU-D. Population: the set of all students in DLSU-D. 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 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 3. Sample is part of the population or a sub-collection of elements drawn from a population. 4. Parameter is a numerical measurement describing some characteristic of a population. 5. Statistic is a numerical measurement describing some characteristic of a sample. 6. Survey is often conducted to gather opinions or feedbacks about a variety of topics. 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. Lecture Notes : Statistics 2009 5 Name:________________________________ Score:___________________ Course/Year/Section:____________________ Teacher:_________________ Exercise 1.2.1 Direction: Identify the population, variable of interest, and type of variable in the following: 1. The dean of COS would like to determine the average weekly allowance of BS Computer Science 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 CLA 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:_________________________________________________________ Lecture Notes : Statistics 2009 6 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:______________