If you like mathematical puzzles or love algebra, try this! Otherwise, just trust that the computational formula for the sum of squares is correct. We have a sample of x values. The sample size is n. Fill in the details for the following steps.Σ(x - x)2=Σ( 2 - 2xx + x2)by binomial expansion =Σx2 - 2xΣ + Σx2by distributive property =Σx2 - 2xΣx + x2adding the same quantity, x, n times, is in fact multiplying it by n =Σx2 - 2x( x) + nx2by substitution, since (Σx)/n = x, hence Σx = nx =Σx2 - x2 + nx2by multiplication, and expansion =Σx2 - x2by addition, combination of alike terms =Σx2 -n (Σ n)2by substitution, since (Σx)/n = x =Σx2 -n ((Σ )2n2)by distributive property =Σx2 -(Σx)2 by multiplication, cancellation

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Description: If you like mathematical puzzles or love algebra, try this! Otherwise, just trust that the computational formula for the sum of squares is correct. We have a sample of x values. The sample size is n. Fill in the details for the following steps.Σ(x -

It is given that the sample size is n.

Answered: If you like mathematical puzzles or…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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If you like mathematical puzzles or love algebra, try this! Otherwise, just trust that the computational formula for the sum of squares is correct. We have a sample of x values. The sample size is n. Fill in the details for the following steps.

Σ(x - x)²

Σ( ² - 2xx + x²)

by binomial expansion

Σx² - 2xΣ + Σx²

by distributive property

Σx² - 2xΣx + x²

adding the same quantity, x, n times, is in fact multiplying it by n

Σx² - 2x( x) + nx²

by substitution, since (Σx)/n = x, hence Σx = nx

Σx² - x² + nx²

by multiplication, and expansion

Σx² - x²

by addition, combination of alike terms

Σx² -

n (

)²

by substitution, since (Σx)/n = x

Σx² -

n (

(Σ )²

n²

)

by distributive property

Σx² -

(Σx)²

by multiplication, cancellation

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