Math Problem Statement
uppose the value of Young's modulus (GPa) was determined for cast plates consisting of certain intermetallic substrates, resulting in the following sample observations: 116.8 115.5 114.9 115.1 115.6 (a) Calculate x. Calculate the deviations from the mean. (Enter your answers to two decimal places.) x 116.8 115.5 114.9 115.1 115.6 deviation
(b) Use the deviations calculated in part (a) to obtain the sample variance and the sample standard deviation. (Round your answers to three decimal places.) s2 =
GPa2 s =
GPa
Solution
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Math Problem Analysis
Mathematical Concepts
Statistics
Sample Mean
Variance
Standard Deviation
Formulas
Sample mean formula: x̄ = (Σxᵢ) / n
Sample variance formula: s² = (Σ(xᵢ - x̄)²) / (n - 1)
Sample standard deviation formula: s = √s²
Theorems
Law of Large Numbers (in the context of variance and mean approximation)
Suitable Grade Level
Undergraduate
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