the mens of 20numbers is 18if3is added to each of the first 10numbers find the means of the new set of 20numbers
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Let the 20 observations be X1 ,X2 ,X3 ,…., X20
Sum of n observations = mean × no. of observations
Sum of 20 observations = 18 ×20
X1 + X2 +X3 + ….+X20 = 360 ….…(1)
When 3 is added to first 10 numbers, then sum of new observations will be
(X1+3)+(X2+3)+(X3+3)+…+(X9+3)+(X10+3)+X11+…+X20 = (X1+X2+X3+….+X20)+3×10
=360 + 30 …….(from 1)
=390
So , mean of new observations = 390÷20 = 19.5
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