Let `x_1 ,x_2 ,….., x_n ` be n observation and let `barx` be their arithmetic mean and ` sigma^2 ` be the variance
statement -1 Variance of ` 2x_! , 2x_2 ,…, 2X_n ` is ` 4 sigma^2 `
Statement -2 arithmatic mean of ` 2x_1 ,2x_2 ,..., 2X_n ` is `4 barx`

Let x_(1),x_(2),..,x_(n) be n observations, and let x be their arithmetic mean and sigma^(2) be the variance Statement 1 : Variance of 2x_(1),2x_(2),..,2x_(n) " is" 4sigma^(2) . Statement 2: Arithmetic mean 2x_(1),2x_(2),..,2x_(n) is 4x.

Let x_1,""x_2,"". . . . . . ,""x_n be n observations, and let bar x be their arithematic mean and sigma^2 be their variance. Statement 1: Variance of 2x_1,""2x_2,"". . . . . . ,""2x_n""i s""4""sigma^2 . Statement 2: Arithmetic mean of 2x_1,""2x_2,"". . . . . . ,""2x_n""i s""4x . (1) Statement 1 is false, statement 2 is true (2) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1 (3) Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1 (4) Statement 1 is true, statement 2 is false

If x_(1),x_(2)……..x_(n) be n observation and barx be their arithmetic mean .Then formula of the standard deviation is given by

Mean of n observations x_1,x_2 ,…., x_n is barx . If an observation x_q is replaced by x'_q , then the new mean is :

Given that barx is the mean and sigma^2 is the variance of n observations x_1,x_2 ,…., x_n . Prove that the mean and variance of the observations ax_1,ax_2 , .., ax_n , are abarx and a^2sigma^2 respectively (a ne 0) .

If sigma^2 is the variance of n observations x_1,x_2 ,…., x_n ,prove that the variance of n observations ax_1,ax_2 ,…, ax_n is a^2sigma^2 , where a ne 0