n 1 n For sample values X1, X2, X, the sample variance is s² = n-1 -Σ (x-x) ², where x = -- Σ x; is the sample n i=1 i=1 mean. (a) Show that the sample variance is unchanged if a constant c is added to or subtracted from each value in the sample. (b) Show that the sample variance becomes c² times its original value if each observation in the sample is multiplied by c.
n 1 n For sample values X1, X2, X, the sample variance is s² = n-1 -Σ (x-x) ², where x = -- Σ x; is the sample n i=1 i=1 mean. (a) Show that the sample variance is unchanged if a constant c is added to or subtracted from each value in the sample. (b) Show that the sample variance becomes c² times its original value if each observation in the sample is multiplied by c.
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter4: Writing Linear Equations
Section: Chapter Questions
Problem 12CR
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Question
I need help with this parts a and b please
![n
1
n
For sample values X1, X2,
X, the sample variance is s² =
n-1
-Σ (x-x) ², where x = -- Σ x; is the sample
n
i=1
i=1
mean.
(a) Show that the sample variance is unchanged if a constant c is added to or subtracted from each value in the
sample.
(b) Show that the sample variance becomes c² times its original value if each observation in the sample is multiplied
by c.
(a) If a constant c is added to or subtracted from each value in the sample, how do the sample values x, change?
Each x
becomes cx;.
remains unchanged.
becomes (x + c).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb7f238f8-1f46-4a1c-b609-d7342775b44d%2F7a645443-4e11-4fa1-be46-c36414818729%2F6rus0q_processed.png&w=3840&q=75)
Transcribed Image Text:n
1
n
For sample values X1, X2,
X, the sample variance is s² =
n-1
-Σ (x-x) ², where x = -- Σ x; is the sample
n
i=1
i=1
mean.
(a) Show that the sample variance is unchanged if a constant c is added to or subtracted from each value in the
sample.
(b) Show that the sample variance becomes c² times its original value if each observation in the sample is multiplied
by c.
(a) If a constant c is added to or subtracted from each value in the sample, how do the sample values x, change?
Each x
becomes cx;.
remains unchanged.
becomes (x + c).
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