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?
Solutions · 1
Official solution
As we know variance does not change with the change of origin. So, here even after adding grace marks 10, the variance will be same.
Let's see with an example,
Assume initial variance \[ = {{\sum {{{\left( {{x_i} - \overline x } \right)}^2}} } \over N}\]
After adding grace marks 10 with each student,
the final variance \[ = {{{\sum {\left[ {\left( {{x_i} + 10} \right) - \left( {\overline x + 10} \right)} \right]} } \over N}^2}\]
\[ = {{\sum {{{\left( {{x_i} - \overline x } \right)}^2}} } \over N}\]
= Initial variance.