Stats & probs 1st summative

• Probability is a branch of mathematics concerning events and numerical descriptions of how likely they are to occur.
• The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur.
• Statistics is a branch of mathematics that concerns the collection, organization, analysis, interpretation, and presentation of data.
• Statistics is defined as a science that studies data to be able to make decisions.
• Statistics is a tool in decision-making process.
• Statistics involves the methods of collecting, processing, summarizing, and analyzing data in order to provide answers or solutions to an inquiry.
• Statistics comes from the word “state” – because governments have been involved in the statistical activities, especially the conduct of censuses either for military or taxation purposes.
• Statistics enables us to characterize persons, objects, situations, and phenomena; explain relationships among variables; formulate objective assessments and comparisons; and make evidence-based decisions and predictions.
• Data collection for Philippine Statistics Authority (PSA) is conducted by the National Statistics Office (NSO), a government agency that conducts censuses and surveys to obtain information about socio-demographic characteristics of the residents of the country.
• Census data are used by the government to make plans.
• Data is viewed as a collection of facts from experiments, observations, sample surveys and censuses, and administrative reporting system.
• Frequency Distribution Table (FDT) is a chart that summarizes values and their frequency, it displays the frequency of each data set in an organized way, it is a way to organize data so that it makes the data more meaningful.
• Examples of discrete random variables include: number of heads obtained when tossing a coin thrice, number of siblings a person has, number of students present in a classroom at a given time.
• A variable is a characteristic that is observable or measurable in every unit of the universe and could be classified as qualitative or quantitative (discrete/continuous).
• A random sample is a subset of objects taken from the population.
• Random means chosen or done without a particular plan or pattern.
• Examples of discrete and continuous variables also include: average temperature in Baguio City for the past 5 days, weight of 8 randomly selected Math books, amount of sugar in a cup of coffee, amount of rainfall (in mm) in different cities in NCR, the number of gifts received by 20 students during Christmas season.
• Discrete random variable is a random variable that can take on a finite number of distinct values (countable/finite/whole number).
• Examples of discrete and continuous variables include: score of a student in a quiz, how long students ate breakfast, time to finish running 100 meter, amount of paint utilized in a building project, the number of death per year attributed to lung cancer, the speed of a car, the number of dropout in a school district in a period of 10 years, the number of voter favoring a candidate, the time needed to finish the test, number of eggs a hen lays.
• Continuous random variable is a random variable that takes infinitely uncountable numbers of possible values, typically measurable quantities (decimal/not specific).
• A random variable is a variable whose value is subject to variations due to chance and is a set of possible different values, each with an associated probability.
• Variables can be classified into Qualitative Variables (categorical variables) and Quantitative Variables (numerical data).
• Discrete data are those data that can be counted, for example, the number of days for cellphones to fail, the ages of survey respondents measured to the next year, and the number of patients in the hospital.
• Continuous data are those that can be measured, for example, the exact height of a survey respondent and the exact volume of some liquid substance.
• A random variable is a variable whose value is subject to variations due to chance and can have a set of possible different values, each with an associated probability.
• A sample space is a collection or a set of possible outcomes of a random experiment, represented using the symbol, “S”.
• The subset of possible outcomes of an experiment is called events.
• A sample space may contain a number of outcomes that depends on the experiment.
• If a sample space contains a finite number of outcomes, then it is known as discrete or finite sample spaces.
• The possible values of a random variable can be found by drawing a table containing the possible outcomes and the values of a random variable.
• The possible values of a random variable can also be found by using a tree diagram.
• The possible values of a random variable can be found by solving a problem using the principle of inclusion and exclusion.
• The possible values of a random variable can be found by solving a problem using the principle of conditional probability.
• The possible values of a random variable can be found by solving a problem using the principle of Bayes' theorem.
• The values of a random variable X can also be found using a Tree Diagram.