Consider three observations a, b, and c such that b = a + c. If the standard deviation of a + 2, b + 2, c + 2 is d, then which of the following is true?

If $$\sum\limits_{i = 1}^n {\left( {{x_i} - a} \right)} = n$$ and $$\sum\limits_{i = 1}^n {{{\left( {{x_i} - a} \right)}^2}} = na$$
(n, a > 1) then the standard deviation of n
observations x₁ , x₂ , ..., x_n is :

If the mean and the standard deviation of the
data 3, 5, 7, a, b are 5 and 2 respectively, then a and b are the roots of the equation :

The mean and variance of 7 observations are 8 and 16, respectively. If five observations are 2, 4, 10, 12, 14, then the absolute difference of the remaining two observations is :