The mean of the data set comprising of 16 observations is 16. If one of the observation valued 16 is deleted and three new observations valued 3, 4 and 5 are added to the data, then the mean of the resultant data, is :

The variance of first 50 even natural numbers is

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given?

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$$\overline x $$.