Question

if x bar is the mean of x1, x2... xn. then for a is not equal to zero . the mean of ax1,ax2,...axn, x1/a,x2/a,.. xn/a is equal to

Answer 1

The mean of a x1 , a x2 ,.....axn = a x bar
and
the mean of x1/a , x2/a ,......xn/a = x bar /a

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Answer 2

the mean of ax1,ax2,...axn = ax bar , Mean of x1/a,x2/a,...xn/a = x bar / a

Mean of ax1,ax2,...axn, x1/a,x2/a,.. xn/a = ((a² + 1)/2a) (x bar)

Step-by-step explanation:

if x bar is the mean of x1, x2... xn.

Then sum of x1, x2... xn.   = n( x bar)

Sum of ax1,ax2,...axn = a (x1 + x2 + .................xn)

= an( x bar)

Mean = an( x bar)/n = a( x bar)

Sum of x1/a,x2/a,...xn/a = (x1 + x2 + .................xn)/a

= n( x bar)/a

Mean = n( x bar)/an = ( x bar)/a

if taking both together  ax1,ax2,...axn & x1/a,x2/a,.. xn/a

number of terms = n + n = 2n

Sum = a(x1 + x2 + .................xn) +  (x1 + x2 + .................xn)/a

= (x1 + x2 + .................xn) (a + 1/a)

=  n( x bar) (a² + 1)/a

Mean =  n( x bar) (a² + 1)/a*2n

=  (x bar) (a² + 1)/2a

= ((a² + 1)/2a) (x bar)

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