Mean of d1,d2,d3...dn
=i=1∑n(n−xi−a)
=−i=1∑nnxi+n−ai=1∑n1
=−x+n−an
=−x−a
And, the mode of d1,d2,d3...dn will be −M−a
Also, we know that the variance σ2 is unaffected by change of origin, hence it remains same.
Let xˉ, M and σ2 be respectively the mean, mode and variance of n observations x1,x2,....,xn and di=−xi−a,i=1,2,....,n, where a is any number.
Statement I: Variance of d1,d2,...,dn is σ2.
Statement II: Mean and mode of d1,d2,....,dn are −xˉ−a and −M−a, respectively.
Held on 19 Apr 2014 · Verified 6 Jul 2026.
Statement I and Statement II are both true
Statement I and Statement II are both false
Statement I is true and Statement II is false
Statement I is false and Statement II is true
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