and 
be respectively the mean, mode and variance of n observations 
and
where is any number. Statement I: Variance of 
is
Statement II: Mean and mode of are
and ? M ? a, respectively.
JEE Main Online Paper (Held On 19 April 2016)
A) Statement I and Statement II are both false
B) Statement I and Statement II are both true
C) Statement I is true and Statement II is false
D) Statement I is false and Statement II is true
Correct Answer: B
Solution :
Mean of 
??.,
Since, 
and we multiply or subtract each observation by any number the mode remains the same. Hence mode of 
i.e. di and xi are same. Now variance of
?.., 
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