Let y1, . ... Yn real numbers, and let n y = 1/√ Σ² ²=1 Yi n their arithmetic mean. Show that for any real number a the formula holds n - n - - Σ (Yi − a)² = Σ (Yi − ÿ)² + n(ÿ − a)² i=1 i=1 Guidance: start from the presentation (yi - a)² = (Yi − ÿ †ÿ − a)² -
Let y1, . ... Yn real numbers, and let n y = 1/√ Σ² ²=1 Yi n their arithmetic mean. Show that for any real number a the formula holds n - n - - Σ (Yi − a)² = Σ (Yi − ÿ)² + n(ÿ − a)² i=1 i=1 Guidance: start from the presentation (yi - a)² = (Yi − ÿ †ÿ − a)² -
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.2: Properties Of Division
Problem 51E
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Transcribed Image Text:Let y1, .
...
Yn real numbers, and let
n
y = 1/√ Σ² ²=1 Yi
n
their arithmetic mean. Show that for any real number a the formula holds
n
-
n
-
-
Σ (Yi − a)² = Σ (Yi − ÿ)² + n(ÿ − a)²
i=1
i=1
Guidance: start from the presentation (yi - a)² = (Yi − ÿ †ÿ − a)²
-
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