Let x = (x1, x2 ..., xi, ..., xn) be a data set with a sample mean x̄ and a sample variance Sx2. Also, let y = (y1, y2 ..., yi, ..., yn) be a data set with a sample mean ȳ and sample variance Sy2. Finally, let z = x - y such that z = (x1 - y1, x2 - y2 ..., xi - yi, ... xn - yn). Show that z̄ = x̄ - ȳ.

Let x = (x1, x2 ..., xi, ..., xn) be a data set with a sample mean x̄ and a sample variance Sx2. Also, let y = (y1, y2 ..., yi, ..., yn) be a data set with a sample mean ȳ and sample variance Sy2. Finally, let z = x - y such that z = (x1 - y1, x2 - y2 ..., xi - yi, ... xn - yn). Show that z̄ = x̄ - ȳ.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Let x = (x₁, x₂ ..., x_i, ..., x_n) be a data set with a sample mean x̄ and a sample variance S_x². Also, let y = (y₁, y₂ ..., y_i, ..., y_n) be a data set with a sample mean ȳ and sample variance S_y². Finally, let z = x - y such that z = (x₁ - y₁, x₂ - y₂ ..., x_i - y_i, ... x_n - y_n).

Show that z̄ = x̄ - ȳ.

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