Statistics and probability

• is a branch of mathematics that deals with the scientific collection, organization, presentation, analysis, and interpretation of numerical data in order to obtain useful and meaningful information.

  Statistics
• refers to the process of obtaining information.

  Collection of data
• refers to the ascertaining manner of presenting the data into tables, graphs, or charts so that logical and statistical conclusions can be drawn from the collected measurements.

  Organization of data
• refers to the process of extracting relevant information from the given data from which numerical description can be formulated.

  Analysis of data
• refers to the task of drawing conclusions from the analyzed data.

  Interpretation of data
• is a statistical method concerned with describing the properties and characteristics of a set.

  DESCRIPTED STATISTICS
• is a statistical method concerned with the analysis of a sample data leading to prediction, inferences, interpretation, or conclusion about the entire population.

  INFERENTIAL STATISTICS
• any quantitative or qualitative information.

  Data
• refers to numerical information obtained from counting or measuring that can be manipulated by any fundamental operation.

  QUANTITATIVE DATA
• refers to descriptive attributes that cannot be subjected to mathematical operations.

  QUALITATIVE DATA
• refers to the totality of all the elements or persons for which one has an interest at a particular time.

  POPULATION
• is a part of a population determined by sampling procedures

  SAMPLE
• is any statistical information or attribute taken from a population.

  PARAMETER
• is any estimate of statistical attributes taken from a sample.

  STATISTIC
• is a specific factor, property, or characteristics of a population ar a sample which differentiates sample or a group of samples from another group.

  VARIABLE
• is a variable that can be obtained by counting.

  DISCRETE VARIABLE
• is a variable that can be obtained by measuring objects or attributes.

  CONTINUOUS VARIABLE
• is a statistic that serves as a representative of the data.

  MEASURES OF CENTRAL TENDENCY OR MEASURE OF AVERAGE
• is a statistic that indicates how close or widespread the data values are.

  MEASURES OF DISPERSION OR MEASURE OF SPREAD
• or arithmetic average is the most important, the most useful and the most widely used measure of central tendency.

  MEAN
• is the middle value in a set of quantities. It separates an ordered set of data into two equal parts. The symbol 𝑥 ̃ will be used to denote the median.

  MEDIAN
• is the value with the most number of frequency.

  MODE
• contains only one mode.

  Unimodal
• contains two modes.

  Bimodal
• contains three or more modes.

  Trimodal or Multimodal
• is a field of mathematics that deals with chance.

  PROBABILITY
• is an activity in which the results cannot be predicted with certainty. Each repetition of an experiment is called a trial.

  Experiment
• is a result of an experiment.

  OUTCOME
• is any collection of outcomes, and a simple event with only one possible outcome.

  EVENT
• is a set S that contains all possible outcomes of the experiment. In any experiment for which the sample space is S, the probability of an event occurring is given by the formula.

  SAMPLE SPACE
• the difference between the highest and lowest values

  RANGE
• the range of the middle half of a distribution.

  INTERQUARTILE RANGE
• average distance from the mean.

  STANDARD DEVIATION
• average of squared distances from the mean

  VARIANCE
• Sum of all probabilities is one

  Probability of each value of a discrete random variable is between 0 and 1 inclusive 0≤𝑃(𝑥)≤1

  can be presented: Tabular Graphical Formula form

  Discrete probability distribution
• It can take on any value in an interval

  Continuous data
• It can only have specific values

  Discrete data
• It is a variable whose possible values are determined by chance It is typically represented by an uppercase letter, usually X

  Random variable
• It can only take a finite or countable number of distinct values.

  Discrete random variable
• can assume an infinite number of values in an interval between two specific values are measurements or dimensions on a continuous scale

  Continuous random variable