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