If mean and standard deviation of 5 observations `x_(1), x_(2), x_(3), x_(4), x_(5)` are 10 and 3, respectively, then the variance of 6 observations `x_(1), x_(2), …, x_(5)` and -50 is equal to

The mean and standart deviation of five observations x_1,x_2,x_3,x_4,x_5 and are 10 and 3 respectively, then variance of the observation x_1,x_2,x_3,x_4,x_5,-50 is equal to (a) 437.5 (b) 507.5 (c) 537.5 (d) 487.5

If, s is the standard deviation of the observations x_(1),x_(2),x_(3),x_(4) and x_(5) then the standard deviation of the observations kx_(1),kx_(2),kx_(3),kx_(4) and kx_(5) is

The mean and standard deviation of 10 observations x_(1), x_(2), x_(3)…….x_(10) are barx and sigma respectively. Let 10 is added to x_(1),x_(2)…..x_(9) and 90 is substracted from x_(10) . If still, the standard deviation is the same, then x_(10)-barx is equal to

If both the mean and the standard deviation of 50 observations x_(1), x_(2),…, x_(50) are equal to 16, then the mean of (x_(1) -4)^(2), (x_(2) -4)^(2), …., (x_(50) - 4)^(2) is k. The value of (k)/(80) is _______.

The means and variance of n observations x_(1),x_(2),x_(3),…x_(n) are 0 and 5 respectively. If sum_(i=1)^(n) x_(i)^(2) = 400 , then find the value of n

If both the mean and the standard deviation of 50 observatios x_(1), x_(2),….x_(50) are equal to 16, then the mean of (x_(1)-4)^(2), (x_(2)-4)^(2),….,(x_(50)-4)^(2) is

If the standard deviation of n observation x_(1), x_(2),…….,x_(n) is 5 and for another set of n observation y_(1), y_(2),………., y_(n) is 4, then the standard deviation of n observation x_(1)-y_(1), x_(2)-y_(2),………….,x_(n)-y_(n) is

The variance of observation x_(1), x_(2),x_(3),…,x_(n) is sigma^(2) then the variance of alpha x_(1), alpha x_(2), alpha x_(3),….,alpha x_(n), (alpha != 0) is

Mean deviation for n observation x_(1),x_(2),…..x_(n) from their mean bar x is given by

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_(3),………….ax_(n) are abarx and a^(2)sigma^(2) , respectively, (a!=0)