GELE Mathematics — Engineering Data Analysis (Probability and Statistics)Concept Map

Concept

Descriptive Statistics

Sub Concepts

• Measures of Central Tendency (Mean, Median, Mode)
• Measures of Dispersion (Variance, Standard Deviation, Range)
• Data Visualization (Histograms, Box Plots)
• Population vs Sample Statistics

Relationship To Central

Summarizes and describes collected data using numerical measures

Concept

Probability

Sub Concepts

• Fundamental Rules (Addition, Multiplication, Complement)
• Conditional Probability
• Independent and Dependent Events
• Mutually Exclusive Events

Relationship To Central

Quantifies uncertainty and likelihood of events in engineering systems

Concept

Counting Techniques

Sub Concepts

• Permutations (Order Matters)
• Combinations (Order Irrelevant)
• Factorial Notation
• Applications to Quality Control

Relationship To Central

Determines number of outcomes and arrangements in probabilistic scenarios

Concept

Probability Distributions

Sub Concepts

• Discrete Distributions (Binomial, Poisson)
• Continuous Distributions (Normal/Gaussian)
• Distribution Parameters (Mean, Variance)
• Z-Standardization and Tables

Relationship To Central

Models behavior of random variables across different engineering contexts

Concept

Inferential Statistics

Sub Concepts

• Hypothesis Testing
• Confidence Intervals
• Sampling Distributions
• Type I and Type II Errors

Relationship To Central

Draws conclusions about populations from sample data with quantified confidence

Concept

Engineering Applications

Sub Concepts

• Quality Control and Process Variation
• Reliability Analysis
• Design of Experiments
• Risk Assessment in Infrastructure

Relationship To Central

Applies statistical methods to solve real civil engineering problems

To

Probability

From

Descriptive Statistics

Strength

strong

Relationship

Statistical summaries (mean, variance) provide parameters for probability distributions

To

Probability Distributions

From

Probability

Strength

strong

Relationship

Probability rules form the foundation for understanding how distributions work and calculating probabilities

To

Probability

From

Counting Techniques

Strength

strong

Relationship

Permutations and combinations are used to count favorable and total outcomes in probability calculations

To

Inferential Statistics

From

Probability Distributions

Strength

strong

Relationship

Distributions model random variables; inference uses these models to estimate population parameters from samples

To

Inferential Statistics

From

Descriptive Statistics

Strength

strong

Relationship

Sample statistics (x̄, s) estimate population parameters (μ, σ) used in hypothesis testing and confidence intervals

To

Engineering Applications

From

Probability Distributions

Strength

strong

Relationship

Normal and binomial distributions model engineering system behavior (loads, strength, defects, reliability)

To

Engineering Applications

From

Counting Techniques

Strength

moderate

Relationship

Combinations used in quality control sampling plans and design of experiments

To

Engineering Applications

From

Inferential Statistics

Strength

strong

Relationship

Hypothesis testing and confidence intervals assess structural safety, material quality, and design margins

To

Probability Distributions

From

Descriptive Statistics

Strength

moderate

Relationship

Histograms and frequency distributions reveal patterns that suggest appropriate probability models

To

Probability Distributions

From

Counting Techniques

Strength

strong

Relationship

Binomial coefficient C(n,x) is fundamental to binomial distribution formula and probability calculations

To

Engineering Applications

From

Probability

Strength

strong

Relationship

Risk assessment, safety factors, and failure probability analysis rely on probability rules and event analysis

To

Engineering Applications

From

Descriptive Statistics

Strength

strong

Relationship

Process control charts, material testing, and system monitoring use mean and standard deviation analysis