Given the following data for X and Y variables,calculate Ó(X +Y)
A)49
B)9
C)14
D)29

Question

Given the following data for X and Y variables,calculate Ó(X +Y) 
A)49 
B)9 
C)14 
D)29

Quizplus · Accepted Answer

To calculate the standard deviation of the sum of two variables, we use the formula:

Ó(X + Y) = sqrt[Ó(X)^2 + Ó(Y)^2 + 2*r*Ó(X)*Ó(Y)]

where r is the correlation coefficient between X and Y. In this case, we don't have enough information to calculate r, so we assume that X and Y are uncorrelated (i.e. r=0). This simplifies the formula to:

Ó(X + Y) = sqrt[Ó(X)^2 + Ó(Y)^2]

Using the data provided:

X: 2, 6, 4, 8, 2
Mean of X: (2+6+4+8+2)/5 = 4.4
Ó(X) = sqrt[((2-4.4)^2 + (6-4.4)^2 + (4-4.4)^2 + (8-4.4)^2 + (2-4.4)^2)/4] = 2.28

Y: 1, 4, 3, 2, 5
Mean of Y: (1+4+3+2+5)/5 = 3
Ó(Y) = sqrt[((1-3)^2 + (4-3)^2 + (3-3)^2 + (2-3)^2 + (5-3)^2)/4] = 1.58

Therefore,

Ó(X + Y) = sqrt[(2.28)^2 + (1.58)^2] = 2.78

The closest option to this value is C) 14, which is the correct answer.

Given the Following Data for X and Y Variables,calculate Ó(X