Statistics and Probability Overview

Statistics Overview

• Statistics is the collection, organization, study, analysis, display, and interpretation of data.
• It provides reasoning and methods for creating and understanding data.

Areas of Statistics

• Descriptive statistics: summarizes or describes data sets.
• Inferential statistics: makes predictions that go beyond data collection.

Sources of Data

• Primary data: collected through surveys, interviews, direct observations.
• Secondary data: collected from newspapers, journals, research papers, panel method, mail survey, project techniques, sociometry.

Methods of Data Collection

• Observation
• Experimentation
• Simulation
• Interviewing

Probability

• Probability is the chance that a particular event will occur.
• An event is an outcome resulting from an experiment.
• Sample space is the set of all possible outcomes or events.

Permutation and Combination

• Permutation: arranging few or all members within a specific order, where the order and details matter.
  • Formula: 𝑛𝑃𝑟 =
• Combination: selecting objects or items from a set, where the order and details don't matter.
  • Formula: 𝑛!(𝑛−𝑟)!𝑛𝐶𝑟 = 𝑛!(𝑛−𝑟)!𝑟!

Random Variable and Probability Distribution

• Random variable: a variable whose value is a real number determined by each element in the sample space.
• Discrete variable: has a countable number of values.
• Continuous variable: has an infinite number of values.

Discrete Probability Distribution

• A table that describes the probability of each discrete random variable value.
• 0 ≤ 𝑃(𝑥) ≤ 1
• Σ𝑥 𝑃(𝑥) = 1

Binomial Distribution

• Describes discrete data in situations where there can only be two results in an experiment: success or failure.
• Formula: 𝑥 𝑛−𝑥 𝑃(𝑥) = (𝑛𝐶𝑥)𝑝 𝑞
• Mean: µ = 𝑛𝑝
• Variance: σ 2 = 𝑛𝑝(1 − 𝑝)

Poisson Distribution

• Counts the number of rare events in a specified time interval or region.
• Formula: 𝑃(𝑋 = 𝑥) = 𝑒 −µ 𝑥!μ
• μ: mean number of occurrences in a particular interval

Normal Distribution

• Describes how the values of a random variable are distributed in a symmetrical bell-shaped graph.
• Parameters: Mean (μ) and Standard Deviation (σ)
• Highest Point: Mean = Median = Mode
• Asymptote: Asymptotic with respect to the horizontal axis
• Shape of Curve: Bell Shape (symmetrical)
• Standard Deviation: measures how flat and wide the curve is
• Total Area: equal to 1

Z-Score

• The number of standard deviations between a value x and the mean of a distribution.
• Formula: 𝑧 = 𝑥−µ σ

Steps in Solving

• Step 1: Draw the standard normal distribution figure (Bell Shape) and represent the area.
• Step 2: Find the value of z score and locate its corresponding value using the table.
• Step 3: Find the appropriate area, solve.
• Step 4: State the conclusion.