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Question

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?


A

Mean

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B

Median

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C

Mode

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D

Variance

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Solution

The correct option is D

Variance


If initially all marks were xi, then
σ21=(xi¯x)2N
Now, each is increased by 10.
σ22=[(xi+10)(¯x10)]2N=σ21
So, variance will not change whereas mean, median and mode will increase by 10.


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