Let x₁, x₂,........., x_n be n observations, and let $$\overline x $$ be their arithematic mean and $${\sigma ^2}$$ be their variance.

Statement 1 : Variance of 2x₁, 2x₂,......., 2x_n is 4$${\sigma ^2}$$.
Statement 2 : : Arithmetic mean of 2x₁, 2x₂,......, 2x_n is 4$$\overline x $$.

If the mean deviation about the median of the numbers a, 2a,........., 50a is 50, then |a| equals

For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is

If the mean deviation of number 1, 1 + d, 1 + 2d,........, 1 + 100d from their mean is 255, then the d is equal to