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Let x(1), x(2),….,x(n) be n observations...

Let `x_(1), x_(2),….,x_(n)` be n observations, and let `barx` be their arithmatic mean and `sigma^(2)` be their variance.
Statement 1 : Variance of `2x_(1),2x_(2),….,2x_(n)` is `4sigma^(2)`
Statement 2 : Arithmatic mean of `2x_(1), 2x_(2),….,2x_(n)` is `4 bar x`.

A

Statement-1 is true, Statement-2 is true.
Statement-2 is not a correct explnation for Statement-1.

B

Statement-1 is true, Statement-2 is false.

C

Statement-1 is false, Statement-2 is true.

D

Statement-1 is true, Statement-2 is ture, Statement-2 is a correct explanation for Statement-1

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Knowledge Check

  • Let x_1,x_2,……,x_n be n observations, and let barx be their arithimetic mean and sigma^2 be their variance. Statement1: Variance of 2x_1, 2x_2,…..,2x_n is 4 alpha^2 Statement2: Arithmetic mean of 2x_1, 2x_2,…..,2x_n is 4 barx .

    A
    Statement-1 is false, Statement-2 is true
    B
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    C
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    D
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  • The geometric mean of numbers observations x_1, x_2, x_3,….,x_n is

    A
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    B
    ` n/(sum_(i=1)^n((1)/(x_i))`
    C
    `(x_1x_2x_3....x_n)^((1)/(n))`
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    C
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    D
    `(barnx-x_(q)+x_(q)')/(n)`

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