Principles of Statistics Lecture Notes 2025 PDF

2025 Principles of Statistics Dr. Mahmoud Sadek Department of Mathematics, Insurance and applied Statistics Faculty of Commerce and business administration Helwan University | Chapter (1) Introduction Text Book Lecture Notes...

2025 Principles of Statistics Dr. Mahmoud Sadek Department of Mathematics, Insurance and applied Statistics Faculty of Commerce and business administration Helwan University | Chapter (1) Introduction Text Book Lecture Notes On: Principles of Statistics Prof. Afaf El- Dash Prof. Essam Abou-Elkasem Assoc. prof. Nagwa Elbehairy Assoc. prof. Rasha Farghaly Assoc. prof. Samah Abo-Elhadid Department of Mathematics, Insurance and applied Statistics Faculty of Commerce and business administration Helwan University i  Chapter (1) Introduction 1.1 What Is Meant by Statistics 1.2 Who Uses Statistics 1.3 Types of Statistics 1.4 Some Definitions 1.5 Types of Variables 1.6 Collecting Data 1.7 Applied Examples 1.8 Exercises 1.1 What Is Meant by Statistics Statistics: group of methods that are used to collect, analyze, present, and interpret data to make effective decisions. 1.2 Who Uses Statistics As noted, statistical techniques are used extensively by marketing, accounting, quality control, and other departments; consumers; professional sports people; hospital administrators; educators; political parties; physicians; and others involved in making decisions. 1.3 Types of Statistics Like almost all fields of study, statistics has two aspects: theoretical and applied. Theoretical or mathematical statistics deals with the development derivation, and proof of statistical theorems, formulas, rules, and laws. Applied statistics involves the applications of those theorems, formulas, rules, and laws to solve real-world problems. We are concerned with applied statistics only. The applied statistics can be divided into two areas: descriptive statistics and inferential statistics. Ch. 1: Introduction 3  Organizing data Displaying data Descriptive statistics Consists of methods for Describing data by using tables, graphs, and summary measures. Inferential statistics Consists of methods that use sample results to help make decisions or predictions about a population. Ch. 1: Introduction 4 1.4 Some Definitions In this section, some main definitions are introduced. (1) Population: A population consists of all elements (or individuals, items, or objects) whose characteristics are being studied. (2) Sample: A portion of the population selected for study is referred to as a sample. (3) Random sample: A sample drawn in such a way that each element of the population has same chance of being selected is called random sample. (4) Element (or item, unit): An element or item of population or sample is a specific subject or object (for example, a person, firm, …, etc.) about which the information is collected. (5) Variable: A variable is a characteristic under study that assumes different values for different elements. In contrast to a variable, the value of a constant is fixed. (6) Observation or Measurement: the value of a variable for an element is called an observation or measurement. (7) Data Set: A data set is a collection of observations on one or more variables. (8) Census and Sample Survey: A survey that includes every member of the population is called census. The techniques of collecting information from a portion of the population is called a sample survey. Ch. 1: Introduction 5  Examples Gender Qualitative or Categorical Names Non-numeric Status an undergraduate cannot be measured student (freshman, junior numerically but divided into or senior) different categories Eye color religious affiliation Types of variables Discrete (Integer) there are no possible intermediate values between consecutive values of a discrete variable Examples Number of cars Quantitative Number of children in a Numeric family assume numerical values Continuous (Decimals or fractions) assume any value over a certain range Examples Age Time Ch. 1: Introduction 6  Scales of Measurement 1. Nominal level 2. Ordinal level 3. Interval level 4. Ratio level 1. Nominal level of data 1. Non-numeric. 2. order is meaningless. Examples Political affiliation Marital status Brands of cars (FIAT. BMW,….) ‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬ 2. Ordinal level of data 1. Non-numeric. 2. Ordering is mandatory. The categories can be coded in this scale of measurement, and these codes refer to superior or inferior ranking. For example, if we code excellent = 1, good = 2, and poor = 3, then we know that 1 means the most superior and 3 indicates the most inferior. Example Consumers rating for a new brand of mobiles (excellent, very good, poor). ‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬ 3. Interval level of data 1. Numeric. 2. The difference between two ranked values is meaningful. 3. There is no natural zero point. Examples Temperature on a day, it 35-38.3 degree in Cairo. Foot size. ‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬ 4. Ratio level of data 1. Numeric. 2. With an inherent zero starting point. 3. The ratio of two values has a meaning. Examples Weight. Income Tire pressure (psi) Ch. 1: Introduction 7 1.6 Collecting Data Once you decided on the type of data – quantitative or qualitative – appropriate for the problem at hand, you will need to collect the data. Generally, you can obtain the data in four different ways: 1. Data from a published source 2. Data from a designed experiment 3. Data from a survey 4. Data collected observationally Sometimes, the data set of interest already been collected for you and is available in a published source, such a book, journal, or newspaper. For example, you may want to examine and summarize the unemployment rates (i.e., percentages of eligible workers who are unemployed) in 30 states in Egypt states. You can find this data set (as well as numerous other data sets). A second method of collecting data involves conducting a designed experiment, in which the researcher events strict control over the units (people, objects or events) in the study. For example, a recent medical study investigates the potential of aspirin in preventing heart attacks. Volunteer physicians were divided into two groups: the treatment group and the control group. In the treatment group, each physician took one aspirin table a day for one year, while each physician in the control group took an aspirin surveys are a third source of data. With a survey, the researcher samples a group of people, Ch. 1: Introduction 8 asks one or more questions and records the responses samples a group of people, asks one or questions, and records the responses. Probably the most familiar type of survey is the political polls conducted by any one of a numbers of organizations and designed to predict the outcome of a political election. Finally, observational studies can be employed to collect data. In an observational study, the researcher observes the experimental units in their natural setting and records the variable (s) of interest. For example, a company psychologist might observe and record the level of “type A” behavior of a sample of assembly lie workers. Similarly, a finance researcher may observe and record the closing stock prices of companies that are acquired by other firms on the day prior to the buyout and compare them to the closing prices on the day the acquisition is announced. Ch. 1: Introduction 9 1.7 Applied Examples (1) Determine which of the following constitute a population and which constitute a sample. a) Assets of five banks selected from a state. b) Number of computers sold during the past month at all computer stores in Cairo. c) Number of VCRs owned by all families. d) Weights of 50 children in a school. Solution a) Sample , b) population c) population , d) sample (2) The following table lists the 1992 total pay (salary, bonus, and other compensation) of the CEOs of five companies Table (1.1) Company Pay (thousands) Vodafone 16.0 El-Misria 11.5 We 10.2 XXA 7.5 XXB 5.1 XXC 2.6 Determine the following: a) Element (item) b) Variable c) Measurement d) Data set Ch. 1: Introduction 10  With reference to above table Solution a) Element: company b) Variable: pay c) Measurement: the value, a variable for an element for example the measurement of Vodafone equal 16.0 d) Data set is a collection of observations (measurements) on variable {16.0, 11.5, 10.2, 7.5, 5.1, 2.6} (3) The following table gives the starting salaries of five recent college graduates. Table (1.2) Name Salary Ahmed $ 30,200 Mohamed $25,500 Fatma $35,200 Hassan $32,350 Ebd Alla $28,500 Explain the meaning of: (a) an item, (b) a variable, (c) a measurement, (d) a data set, With reference to the above table. Solution: a) student , b) salary c) 30,200 or 25,500 … etc. d) {30,200, 25,500, 35,200, 32,350, 28,500} Ch. 1: Introduction 11