All 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 As we know, mean, median and mode will increase by 10
Now check the variance,
Variance =σ2=∑(xi−¯¯¯x)2N
Now increase the xi and ¯¯¯x by 10 ⇒σ2=∑[(xi+10)−(¯¯¯x+10)]2N ⇒σ2=∑(xi−¯¯¯x)2N
Hence, variance is same