Statistics and Probability PDF

Statistics and Probability Dr. Asmaa Eltoony Dr. Salma Shatta  Chapters Chapter 1: Some Basic Concepts Chapter 2: Basic Probability Concepts Chapter 3: Discrete Distributions Chapter 4: Continuous Distributions Chapter 5: Joint Discrete Probability Distribut...

Statistics and Probability Dr. Asmaa Eltoony Dr. Salma Shatta  Chapters Chapter 1: Some Basic Concepts Chapter 2: Basic Probability Concepts Chapter 3: Discrete Distributions Chapter 4: Continuous Distributions Chapter 5: Joint Discrete Probability Distributions  01 Introduction  Main concepts Statistic Probability Statistics: Is the science of : collecting, organizing, Biostatistics: presenting, If the information is obtained from analyzing, and biological and medical sciences, then interpreting data we use the term biostatistics. (Application) to assist in making decisions and drawing conclusions.  Statistical process Analysis collecting interpreting data Organizing Conclusion presenting making decisions  Why Study Statistics? No matter what line of work you select, you will find yourself faced with decisions where an understanding of data analysis is helpful. In order to make an informed decision, you will need to able to: 1. Determine whether the existing information is sufficient or additional information is required. 2. Gather additional information, if it is needed, in such away that it is does not provide misleading results. 3. Summarize the information in a useful informative manner. 4. Analyze the available information. 5. Draw conclusions and make inferences while assessing the risk of an incorrect conclusion.  Statistics is the language of science and data. Data: The raw material of Statistics is data. Data can be defined as a collection of facts or information from which conclusions may be drawn. For example: When a botanist counts the number of Petals on a flower (counting). When a Zoologist weights a cow (measurement).They’re simple  Classification of statistical data Statistical data Quantitative Qualitative (Numerical) ) Categorical) Continuous Discrete Ordinals Nominals  Qualitative data Quantitative data is descriptive information is numerical information (numbers: weights, ages, …). (words: nationalities, occupations, …). Quantitative data can also be Discrete or Continuous: Discrete data can only take certain values (like whole numbers) Examples include colors, names, labels, and other non-numeric Continuous data can take any value (within a range) attributes. Examples include Age, Height, Weight Test Scores, Income, Temperature, Distance, Sales Figures, Survey Ratings Example: What do we know about Arrow the Dog? Qualitative: He is brown and black He has long hair He has lots of energy Quantitative: Discrete: o He has 4 legs o He has 2 brothers Continuous: o He weighs 25.5 kg o He is 565 mm tall Variable: it is a characteristic that takes on different values in different persons, places, or things. For example: heart rate, the heights of adult males, the weights of insects, the ages of trees seen in a forest.  1) Quantitative Variables: A quantitative variable is a characteristic that can be measured. The values of a quantitative variable are numbers indicating how much or how many of something. Examples: (i) Family Size (ii) No. of patients (iii) Weight (iv) height (a) Discrete Variables: (b) Continuous Variables: There are jumps or gaps between the values. There are no gaps between the values. A continuous variable can have any value within a Examples: - Family size (x = 1, 2, 3, … ) certain interval of values. - Number of patients (x = 0, 1, 2, 3, … ) Examples: - Height (140 < x < 190) - Blood sugar level (10 < x < 15) 2) Qualitative Variables: The values of a qualitative variable are words or attributes indicating to which category an element belong. Examples: - Blood type, Nationality , Students Grades ,Educational level (a) Nominal Qualitative Variables: (b) Ordinal Qualitative Variables: A nominal variable classifies the observations An ordinal variable classifies the observations into various mutually exclusive and collectively into various mutually exclusive and collectively non-ranked categories. ranked categories. The values of an ordinal Examples: Blood type (O, AB, A, B) variable are categories that can be ordered Nationality (Saudi, Egyptian, British, …) Examples: Educational level (elementary, Sex (male, female) intermediate, …) Students grade (A, B, C, D, F)  Types of statistics Descriptive Statistics: are the methods of collecting, organizing, summarizing and measuring the collected data. Inferential statistics: methods which gives information about a population based on a sample, that is the process of using data obtained from a sample to make estimates or test hypotheses about the characteristics (parameter) of a population to all the production of the factory, but it is enough to check a sample of it on condition that this sample must represent the production of this factory completely, then we can generalize the results for all the production.  Populations and Samples Population: It is the collection of all possible objects or measurements of interest. Sample: Is a part of the population of interest Data Collection and Sampling Techniques Data can be collected in a variety of ways. One of the most common methods is through the use of surveys. Surveys can be done by using a variety of methods. Three of the most common methods are the telephone survey, the mailed questionnaire, and the personal interview. Researchers use samples to collect data and information about a particular variable from a large population. Using samples saves time and money and in some cases enables the researcher to get more detailed information about a particular subject. Random sample: is the sample whose elements are selected from the elements of a population. In this sample, each element must get the same chance of selecting. One such method is to number each subject in the population. Then place numbered cards in a bowl, mix them thoroughly, and select as many cards as needed. The subjects whose numbers are selected constitute the sample.  Stratified Sampling Definition: Divides the population into groups (strata) based on important characteristics, then samples from each group. Method: Randomly select samples within each stratum. Example: A college president surveys first-year and second-year students separately to compare opinions. Cluster Sampling Definition: Divides the population into clusters (e.g., geographic areas or schools), then randomly selects entire clusters. Method: All members of selected clusters are included in the sample. Example: A researcher randomly selects 2 out of 10 apartment buildings and surveys all residents in those buildings. Differences Stratified Sampling: Ensures representation from each group. Cluster Sampling: Focuses on entire clusters, often used for large populations or geographic areas. 1. What is the primary purpose of statistics? - A) To collect data - B) To assist in making decisions and drawing conclusions - C) To present data in graphs - D) To memorize facts Answer: B 2. What term is used for data obtained from biological and medical sciences? - A) Inferential Statistics B) Descriptive Statistics - C) Biostatistics D) Demographics Answer: C 3. Which of the following is an example of discrete data? A) Height of students B) Number of patients in a hospital C) Weight of apples D) Blood sugar levels Answer: B 4. What is stratified sampling? A) Sampling from a random selection of clusters B) Dividing the population into strata and sampling from each C) Collecting data from the entire population D) Using only one group for sampling Answer: B True or False 1. Statistics is only concerned with collecting data. Answer: False 2. Qualitative data can be number. Answer: False 3. Cluster sampling involves selecting entire groups rather than individual subjects. Answer: True 4. A population includes all possible measurements of interest. Answer: True 5. Inferential statistics is used to summarize data. Answer: False (This is the role of descriptive statistics.) Thanks!