Introduction to Statistics Still John F. Reyes

Definition 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: It refers to actual numbers derived from data and the other refers to statistics as a method of analysis.

Definition of Statistics Statistics – is the theory and method of collecting, organizing, presenting, analyzing and interpreting data. Statistics is a collection of quantitative data, such as statistics of crimes, statistics on enrolment, statistics on unemployment, and the like.

Divisions of Statistics Descriptive Statistics deals with the methods of organizing, summarizing and presenting a mass of data so as to yield meaningful information. Inferential Statistics deals with making generalizations about a body of data where only a part of it is examined. This comprises those methods concerned with the analysis of a subset of data leading to predictions or inferences about the entire set of data.

Divisions of Statistics Examples: A bowler wants to find his bowling average for the past 12 games. Ans: descriptive statistics A manager would like to predict based on previous years’ sales, the sales performance of a company for the next five years. Ans: inferential statistics

Divisions of Statistics Examples: 3. A politician would like to estimate, based on an opinion poll, his chance for winning in the upcoming senatorial election. Ans: inferential statistics 4. A teacher wishes to determine the percentage of students who passed the examination. Ans: descriptive statistics

Basic Statistical Terms 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. Ex: The researcher would like to determine the number of female BSCS students in Cavite State University-Carmona. Population: The set of all students in Cavite State University-Carmona.

Basic Statistical Terms Variable is a characteristic of interest measurable on each and every individual in the universe, denoted by any capital letter in the English alphabet, is called a variable. Types of Variable Qualitative Variable consists of categories or attributes, which have non- numerical characteristics. Quantitative Variable consists of numbers representing counts or measurements.

Basic Statistical Terms Examples: Qualitative Variables Examples are classifications, year level, sex and subjects enrolled this semester. Quantitative Variables Variables for Population: S = no. of students who are smoking E = no. of students who like English

Classification of Quantitative Variable Discrete Quantitative Variable results from either a finite number of possible values or a countable number of possible values. Ex: 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. Ex: height, weight, grade point average, and time.

Basic Statistical Terms Sample is a 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.

Basic Statistical Terms 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.

Exercises Identify the population, variable of interest and type of variable in the following: A group of students taking Statistics conducted a study on the effect of boy-girl relationship to the academic performance of the students. The dean of the College of Science would like to know the number of students who are smoking. A statistics teacher, Mr. Reyes would like to determine whether the number of students in a class at the start of the semester can determine the number of failures.

Exercises Identify each statement as having discrete or continuous data/variable. Among 1,500,000 microcomputer chips made by Motocolla, 2 are found to be defective. Yesterday’s records show that 25 students were absent. Radar on EDSA indicated that the driver was going 150 kph when ticketed for speeding. Upon completion of a diet and exercise program, Tony weighed 12.37 lbs. less than when he started the program.

Levels of Measurement 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

Levels of Measurement 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

Levels of Measurement 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 °C)

Levels of Measurement 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 Width Area Weekly allowance