Question

The mean of 15 observations is 25 if each observation is multiplied by 4,then mean of new observation is

Answer 1

X1,X2,X3,X4,X5.........X15/15=25
=> X1,X2,X3,X4,X5.......X15 = 25×15
=> X1,X2,X3.........X15 = 375

New mean = 4 × (375/15) = 4 ×25 = 100

Answer 2

Hii ,

Let the fifteen observations are X1,X2,X3,X4....X15 .

Mean = Sum of observations / Number of obve

25 = X1+X2+X3+X4+.......X15/15

X1 + X2 + X3 + X4+.......X15 = 25 × 15

X1 + X2 + X3 + X4+.......X15 = 375.

Each observations multiplied by 4 then new observations are X1×4 , X2×4 , X3×4.....X15×4

Mean=Sum of observations/No of observations

Mean = X1×4+X2×4+X3×4........X15×5/15

Mean = 4 ( X1+X2+X3+X4......X15)/15

Mean = 4 × 375/15

Mean = 4× 25

Mean = 100.

Hence,

New mean is 100.

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