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

The standard deviation of first 10 natural numbers is

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

The mean of 100 observations is 50, and their standard deviations is 5. The sum of all squares of all the observations is

Let x₁, x₂, ……x_n, be n observations. Let y_i = ax_i + b for I = 1, 2, ….., n, where a and b are constant. If the mean of is 48 and their standard deviation is 12, the mean of is 55 and standard deviation of is 15, the values of a and b are