Statistics 01 (1) PDF

Chapitre 01: Introduction to statistics What is Statistics? Why Study Statistics? Key Concepts in Statistics. Exercises. 02  What is Statistics? Statistics is a branch of mathematics that deals with the collection, anal...

Chapitre 01: Introduction to statistics What is Statistics? Why Study Statistics? Key Concepts in Statistics. Exercises. 02  What is Statistics? Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It provides methods to summarize and interpret data, allowing us to draw meaningful conclusions and make decisions in the face of uncertainty. Statistics plays a crucial role in various fields, including science, business, economics, social sciences, and government, where it helps in understanding complex phenomena, making predictions, and supporting informed decision-making. 03  Why Study Statistics? Statistics helps in gathering information about the appropriate quantitative data; It depicts the complex data in graphical form, tabular form and in diagrammatic representation to understand it easily; It provides the exact description and a better understanding; It helps in designing the effective and proper planning of the statistical inquiry in any field; It gives valid inferences with the reliability measures about the population parameters from the sample data; It helps to understand the variability pattern through the quantitative observations. 04  Key Concepts in Statistics To learn the basic definitions used in statistics and some of its key concepts. We begin with a simple example. There are millions of passenger automobiles in Algeria. What is their average value? It is obviously impractical to attempt to solve this problem directly by assessing the value of every single car in the country, add up all those values, then divide by the number of values, one for each car. In practice the best we can do would be to estimate the average value.  05 A natural way to do so would be to randomly select some of the cars, say 200 of them, ascertain the value of each of those cars, and find the average of those 200 values. The set of all those millions of vehicles is called the population of interest, and the number attached to each one, its value, is a measurement. The average value is a parameter: a number that describes a characteristic of the population, in this case monetary worth. The set of 200 cars selected from the population is called a sample, and the 200 numbers, the monetary values of the cars we selected, are the sample data. The average of the data is called a statistic: a number calculated from the sample data. This example illustrates the meaning of the following definitions. 06 Population Definition: in statistics, population is the complete collection of items or individuals from which data is gathered for a specific statistical study. This can include various entities such as people, items, events, or organizations. The population serves as the comprehensive data source for the study, constituting the entirety of the information under examination.  07 Sample Definition: a sample is a random selection of members of a population. It is a smaller group drawn from the population that has the characteristics of the entire population. The observations and conclusions made against the sample data are attributed to the population as a whole. 08 Figure01: populatio vs sample 09  Population Sample Advertisements for IT jobs in The top 50 search results for Algeria advertisements for IT jobs in Algeria on May 1, 2023 Undergraduate students in Algeria 300 undergraduate students from three Algerian universities who volunteer for your psychology research study All countries of the world Countries with published data available on birth rates and GDP since 2000 Table 01: populatio vs sample 10 Descriptive statistics  Definition: descriptive statistics is a branch of statistics that involves the collection, interpretation, analysis, presentation, and organization of data. Its primary purpose is to describe and summarize the main features of a dataset, providing meaningful insights into the underlying patterns, trends, and characteristics of the information at hand. 11 Inferential Statistics  Definition: inferential statistics is a branch of statistics that involves drawing conclusions, making predictions, and making inferences about a population based on a sample of data taken from that population. Unlike descriptive statistics, which merely summarize and describe the features of a dataset. 12 Qualitative Variables  Definition: qualitative variables are variables for which there is no natural numerical scale, but which consist of attributes, labels, or other non-numerical characteristics. such as hair color, eye color, gender, and so on. 13 Nominal Variables  Definition: nominal variables are qualitative variables that have no inherent order or ranking. They are used to classify data into distinct categories without any numerical significance. Examples: ▪Gender: Male, Female ▪Color: Red, Blue, Green, Yellow ▪Religion: Muslim, Christian, Jewish, Buddhist 14 Ordinal Variables  Definition: ordinal variables are also qualitative variables, but they have a natural order or ranking among their categories. While they cannot be measured numerically, their categories can be compared in terms of greater or lesser value. Examples: ▪Educational Level: Elementary, Middle, High School, College, Graduate ▪Economic Status: Low, Middle, High ▪Customer Satisfaction: Very Dissatisfied, Dissatisfied, Neutral, Satisfied, Very Satisfied 15 Quantitative Variables  Definition: quantitative variables are variables represented numerically, including anything that can be counted, measured, or given a numerical value. such as height, weight, shoe size, and so on. 16 Discrete Variables  Definition: discrete variables are a type of quantitative variable in statistics that represent distinct, separate values. These variables can only take on specific, isolated numerical values and are often counted in whole numbers. Discrete variables have clear and distinct categories, and there are no intermediate values between these categories. For example, the number of students in a classroom, or the count of cars passing through an intersection in a given time are all examples of discrete variables. In each case, the variable can only take on specific, distinct numerical values, and there are no fractional or intermediate values between these whole numbers. 17 Continuous Variables  Definition: continuous variables are a type of quantitative variable in statistics that can take on an infinite number of values within a specific range. These variables are measured and can represent any numerical value, including fractional and decimal values. Examples of continuous variables include height, weight, temperature, and time. For instance, a person's height can be 1.75 meters, 1.752 meters, or any value in between, and it can be measured with a high degree of precision. Similarly, temperature can be 23.5 degrees Celsius, 23.52 degrees Celsius, and so on. 18 Exercise 01: Identify each of the following data sets as either a population or a sample: a.The grade point averages (GPAs) of all students at a college. b.The GPAs of a randomly selected group of students on a college campus. c.The ages of the Supreme Court Justices of Algeria on January 1, 2025. d.The gender of every second customer who enters a movie theater. 19 Answer: a. Population. b.Sample. c. Population. d.Sample. 20 Exercise 02: a.A teacher wishes to know whether the males in his/her class have more conservative attitudes than the females. A questionnaire is distributed assessing attitudes and the males and the females are compared. Is this an example of descriptive or inferential statistics? b.A researcher selects a random sample of 200 people to study their voting preferences and uses the findings to make predictions about the voting preferences of the entire country. Is this an example of descriptive or inferential statistics? 21 c.A researcher surveys a group of 500 employees in a company to  understand their job satisfaction levels and then presents the average job satisfaction score for the surveyed employees. Is this an example of descriptive or inferential statistics? d.A health researcher analyzes the medical records of patients in a hospital and calculates the percentage of patients who have a particular medical condition. Is this an example of descriptive or inferential statistics? 22 Answer: a.In this example, the teacher simply analyzes and summarizes the attitudes of males and females separately, it is an example of descriptive statistics. b.In this example, the researcher selects a random sample of 200 people to study their voting preferences and uses the findings to make predictions about the voting preferences of the entire country, which is an example of inferential statistics. 23 c.In this example, the researcher summarizes the job satisfaction levels of the surveyed employees without making predictions  about the job satisfaction of employees in other companies. It is descriptive statistics because it focuses on describing the surveyed group. d. In this example, the health researcher is describing the prevalence of a specific medical condition within the group of patients whose records were analyzed. There are no inferences being made about a larger population; rather, the focus is on summarizing the data at hand, which is an example of descriptive statistics. 24 Exercise 03: In each statement, tell whether the descriptive or inferential statistic has been used: a.By 2040 at least 3.5 billion people will run short of water (World Future Society). b.Nine out of ten of the job fatalities are men. c.Expenditures for the cable industry were 5.66 billion in 1996. d.Allergy therapy makes bees go away. e.Drinking decaffeinated coffee can raise cholesterol levels by 7%. f.The national average annual medicine expenditure per person is $1052. g.Experts say the mortgage rates may soon hit bottom. 25 Answer: a.Inferential. b.Descriptive. c.Descriptive. d.Inferential. e.Inferential. f.Descriptive. g.Inferential. 26 Exercise 04: Identify the following data as either quantitative or qualitative: a.The genders of the first 40 newborns in a hospital one year. b.The natural hair color of 20 randomly selected fashion models. c.The ages of 20 randomly selected fashion models. d.The fuel economy in miles per gallon of 20 new cars purchased last month. e.The political affiliation of 500 randomly selected voters. 27 Answer: a.Qualitative. b.Qualitative. c.Quantitative. d.Quantitative. e.Qualitative. 28 Exercise 05: Identify the following data as either quantitative or qualitative: a. The 30 high-temperature readings of the last 30 days. b. The scores of 40 students on an English test. c. The blood types of 120 teachers in a middle school. d. The last four digits of social security numbers of all students in a class. e. The numbers on the jerseys of 53 football players on a team. 29 Answer: a.Quantitative. b.Quantitative. c.Qualitative. d.Qualitative. e.Qualitative. 30 Exercise 06: Classify each variable using the appropriate terms from the following list: qualitative (nominal or ordinal), quantitative (continuous or discrete). a.Weight (in grams) of tomatoes at a grocery store. b.Number of times person checks their e-mail per day. c.Political party that people voted for in the last provincial election. d.Voter participation in past federal elections, as a percentage. e.Daily temperature (in degrees Fahrenheit) for last August. f.Letter grades (A, B, C, D, or F) that an English 100 class received on their essays.  31 Answer a.Quantitative, continuous. b.Quantitative, discrete. c.Qualitative, nominal. d.Quantitative, continuous. e.Quantitative, continuous. f.Qualitative, ordinal. 32