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?

The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 respectively. Each of these 10 observations is multiplied by $p$ $$ and then reduced by $$ $q$ , where $p=0$ $$ and $q\ne 0$ $$ . If the new mean and new s.d. become half of their original values, then $q$ $$ is equal to:

The mean and variance of 10 observations were calculated as 15 and 15 respectively by a student who took by mistake 25 instead of 15 for one observation. Then, the correct standard deviation is