JEE Main · 2013 · 07 Apr 2013 · Offline · Statistics

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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)median
(B)mode
(C)variance✓ Correct
(D)mean

Answer: (C)

Solution

Adding the same ten marks to every score shifts the whole distribution without stretching it. The mean rises by ten as well, so each deviation

x_{i} - \overset{x}{ˉ}

is left untouched, and since variance is built from those deviations,

σ^{2} = \frac{\sum ( x _{i} - x ˉ ) ^{2}}{n}

, it does not change. The mean, median and mode each move up by ten; only the variance stays put.

JEE Main · 2013 · 07 Apr 2013 · Offline · Single correct option

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