Chapter 14.2, Problem 2LC

### Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

Chapter
Section

### Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

# Calculate the sum of products of deviations (SP) for the following set of scores. Use the definitional formula and then the computational formula. Verify that you get the same answer with both formulas. X Y 0 1 4 3 5 3 2 2 4 1

To determine

To calculate: The sum of products of deviations (SP) and verify if the answer is the same if computed by definitional formula and computational formula.

SP=+5,Which is the same using both formulae.

Explanation

Given Info:

Following set of scores are given:

 X Y 0 1 4 3 5 3 2 2 4 1 15 10

Calculation:

The definitional formula for SP is:

SP=(XMx)(YMy)

Where

Mx=mean of X=3My=mean of Y=2

 X Y (X−Mx) (Y−My) (X−Mx)(Y−My) 0 1 -3 -1 3 4 3 1 1 1 5 3 2 1 2 2 2 -1 0 0 4 1 1 -1 -1 +5=SP

Thus, SP value by using definitional formula is +5.

The computational formula is:

SP=XYXYn

 X Y XY 0 1 0 4 3 12 5 3 15 2 2 4 4 1 4 15 10 35

SP=35(15)(10)5SP=+5

Thus, SP value by using computational formula is +5.

Thus, value of SP is same for both formulas.

Concept

Sum of product deviation (SP):

Sum of products of deviations (SP) is given by

SP=×4xyn

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