Consider the following for the two (02) items that follow:
The sum and the sum of squares of the observations corresponding to length $X$ (in cm) and weight $Y$ (in gm) of 50 tropical tubers are given as $\Sigma X = 200$ , $\Sigma Y = 250$ , $\Sigma X^2 = 900$ and $\Sigma Y^2 = 1400$ .

Which one of the following is correct?

Question

Consider the following for the two (02) items that follow:
The sum and the sum of squares of the observations corresponding to length

X

(in cm) and weight

Y

(in gm) of 50 tropical tubers are given as

\Sigma X = 200

,

\Sigma Y = 250

,

\Sigma X^2 = 900

and

\Sigma Y^2 = 1400

.

Which one of the following is correct?

Quantrex Academy · Accepted Answer

Correct answer: B. Variance (X) < Variance (Y)

Given n = 50 , X = 200 , Y = 250 , X^2 = 900 , and Y^2 = 1400 . The variance of X is calculated as: Var(X) = ( X^2)/(n) - (( X)/(n))^2 Var(X) = (900)/(50) - ((200)/(50))^2 Var(X) = 18 - (4)^2 = 18 - 16 = 2 The variance of Y is calculated as: Var(Y) = ( Y^2)/(n) - (( Y)/(n))^2 Var(Y) = (1400)/(50) - ((250)/(50))^2 Var(Y) = 28 - (5)^2 = 28 - 25 = 3 Comparing the variances, we get Var(X) Answer: Variance (X) < Variance (Y)

Consider the following for the two (02) items that follow: The sum...

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