Discussion Forum

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?

Answer:

Explanation:

If initially  all marks were x₁, then 

$\sigma^{2}_{1}=\frac{\sum(x_{i}-\overline{x})^{2}}{N}$

 Now, each is increased by 10

   $\therefore$      $\sigma^{2}_{1}=\frac{\sum(x_{i}+10)-(\overline{x}+10))^{2}}{N}=\sigma^{2}_{1}$

  So, variance will not change whereas mean, median and mode will increase by 10