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
Definition: The middle value when data is arranged in ascending or descending order.
Calculation Steps:
Example: Bearing life cycle data: [120, 135, 140, 142, 150] Median = 140
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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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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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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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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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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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Definition: A graphical representation showing the distribution of data through quartiles.
Key Components:
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Definition: A graphical representation of data distribution using rectangular bars.
Key Features:
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