Standard deviations for first 10 natural numbers is

Let x₁, x₂, x₃, x₄, x₅ be the observations with mean m and standard deviation s.

The standard deviation of the observations kx₁, kx₂, kx₃, kx₄, kx₅ is

Let x₁, x₂, ... x_n be n observations. Let w_i = lx_i + k for i = 1, 2, ...n, where l and k are constants. If the mean of x_i’s is 48 and their standard deviation is 12, the mean of w_i’s is 55 and standard deviation of wi’s is 15, the values of l and k should be

Consider the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. If 1 is added to each number, the variance of the numbers so obtained is

Consider the first 10 positive integers. If we multiply each number by –1 and then add 1 to each number, the variance of the numbers so obtained is