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JEE Main 2013 Paper

Section: Mathematics

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Question : 35 of 90

Marks: +1, -0

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 ?

median
mode
variance
mean

Solution:

Variance is not changed by the change of origin.

Alternate Solution:

\sigma = \sqrt{ \frac{ \sum \left| x-\overset{-}{x} \right|^2 }{ n } }

for

y = x + 10 \Rightarrow \overset{-}{y} = \overset{-}{x} + 10

\sigma_1 = \sqrt{ \frac{ \sum \left| y+10-\overset{-}{y}-10 \right|^2 }{ n } } = \sigma = \sqrt{ \frac{ \sum \left| y-\overset{-}{y} \right|^2 }{ n } } = \sigma

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