Question

If both mean and the standard deviation of 50 observations x1, x2, x3, ...X50are equal to 16. Then the mean of (x1-4)2 ,(x2-4)2,(x3-4)2,........,(x50-4)2 is

Answer 1

sorry bro I didn't now the answer so sorry bro

Answer 2

The mean of the new observations is equal to 24

Given the standard deviation and mean of 50 observations x1, x2, x3, ...X50 are equal to 16

Mean = sum of observations / no. of observations

Mean = (x1+x2+x3...........+X50)/50

=> 16 × 50 = (x1+x2+x3...........+X50)

=> (x1+x2+x3...........+x50) = 800

Now , the new observations are

(x1-4)2 ,(x2-4)2,(x3-4)2,........,(x50-4)2.

Mean =((x1-4)2 +(x2-4)2 +(x3+4)2 + ........+(x50-4)2) / 50

=> Mean = ((2 x1 +2 x2+2 x3 + ........+2 x50) - 8 × 50) / 50

=> Mean = (2×800 - 400)/50

=> Mean = 24

The mean of the new observations = 24