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Question
If ¯x is the mean of x1,x2,xn, then for a≠0, the mean of ax1,ax2,axn,x1a,x2a,..xna
If ¯x is the mean of x1,x2,xn, then for a≠0, the mean of ax1,ax2,axn,x1a,x2a,..xna
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Solution
The correct option is C (a+1a)¯xn
x1+x2+x3....xnx=¯x
ax1+ax2+ax3....axn+x1a+x1a....xna2n
=a[x1+x2....xn]+1a[x1+x2.....xn]2n
=[a+1a][x1+x2.....xn]2n=[a+1a][n¯x]2n
=(a+1a)¯xn
x1+x2+x3....xnx=¯x
ax1+ax2+ax3....axn+x1a+x1a....xna2n
=a[x1+x2....xn]+1a[x1+x2.....xn]2n
=[a+1a][x1+x2.....xn]2n=[a+1a][n¯x]2n
=(a+1a)¯xn
Suggest Corrections
0
is
the mean and σ2
is the variance of n observations x1, x2
… xn. Prove that the mean and
variance of the observations ax1, ax2,
ax3 …axn are
and a2 σ2,
respectively (a ≠ 0).