Module 2: Descriptive Statistics for Engineers

Supporting Lectures:
EGN3443 Module 2 - Descriptive Statistics


1. Measures of Central Tendency

Mean (Arithmetic Average)

Definition: The sum of all values divided by the total number of values.

Formula: μ = (Σx) / n

Example Calculation: Suppose you're measuring the tensile strength of steel samples: Measurements: 450 MPa, 475 MPa, 460 MPa, 465 MPa, 455 MPa Mean = (450 + 475 + 460 + 465 + 455) / 5 = 461 MPa

Median

Definition: The middle value when data is arranged in ascending or descending order.

Calculation Steps:

  1. Sort values from lowest to highest
  2. If odd number of values, take the middle value
  3. If even number of values, take the average of the two middle values

Example: Bearing life cycle data: [120, 135, 140, 142, 150] Median = 140

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Mode

Definition: The value that appears most frequently in a dataset.

Example: Failure times of electronic components: [10, 12, 15, 12, 10, 15, 12] Mode = 12 (appears most often)

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2. Measures of Dispersion

Range

Definition: The difference between the maximum and minimum values in a dataset.

Formula: Range = Maximum Value - Minimum Value

Example: Temperature readings: [22°C, 25°C, 18°C, 30°C, 20°C] Range = 30°C - 18°C = 12°C

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Variance

Definition: A measure of variability that quantifies how far a set of numbers is spread out.

Population Variance Formula: σ² = Σ(x - μ)² / N

Sample Variance Formula: s² = Σ(x - x̄)² / (n-1)

Example Calculation: Machine part measurements: [10.2, 10.5, 10.3, 10.4, 10.1] Mean = 10.3 Variance = [(10.2-10.3)² + (10.5-10.3)² + (10.3-10.3)² + (10.4-10.3)² + (10.1-10.3)²] / 4 ≈ 0.01

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Standard Deviation

Definition: The square root of variance, measuring the amount of variation in a dataset.

Formulas:

Example: Using previous machine part measurements Standard Deviation = √0.01 ≈ 0.1

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3. Data Visualization Techniques

Stem-and-Leaf Plots

Definition: A method of displaying numerical data that shows the distribution of values.

Example: Bearing diameter measurements (mm): Stem | Leaf 24 | 5, 7, 8 25 | 1, 3, 6 26 | 0, 2, 4

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Box Plots

Definition: A graphical representation showing the distribution of data through quartiles.

Key Components:

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Histograms

Definition: A graphical representation of data distribution using rectangular bars.

Key Features:

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4. Interpreting Statistical Summaries in Engineering

Practical Considerations:

Recommended Resources:

We will:

  1. Learn formulas
  2. Practice calculations
  3. Use statistical software (Excel, R, mostly Python)
  4. Apply to real-world engineering scenarios