Q.

If the arithmetic mean of the numbers x1,x2,x3,…,xn is x¯ ,  then the arithmetic mean of the numbers ax1+b,ax2+b , ax3+b,…,axn+b,  where a,b are two constants, would be

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a

x

b

nax+nb

c

ax

d

ax+b

answer is D.

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Detailed Solution

Required Mean=ax1+b+ax2+b+⋯+axn+bn=ax1+x2+⋯+xnn+b=ax¯+b∵x1+x2+⋯+xnn=x¯
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If the arithmetic mean of the numbers x1,x2,x3,…,xn is x¯ ,  then the arithmetic mean of the numbers ax1+b,ax2+b , ax3+b,…,axn+b,  where a,b are two constants, would be