The mean of the data set comprising of 16 observations is 16. If one of the observation valued 16 is deleted and three new observations valued 3, 4 and 5 are added to the data, then the mean of the resultant data, is :
(1) 16.8
(2) 16.0
(3) 15.8
(4) 14.0

Options

A. 15.8
B. 14
C. 16.8
D. `16.0`

Answer

B

Explanation

Let `x_(1),x_(2),x_(3), …, x_(16)` be 6 observations of the given data set.It is given that the mean of these observations is 16.
`therefore (x_(1)+x_(2)+x_(3)+ ...+x_(16))/(16)=16`
`rArr x_(1)+x_(2)+x_(3)+ ...+x_(16)=256`
Let `x_(16)=16.` If this observations is deleted and three new observations valued 3, 4 and 5 are added to the data, then the mean of 18 observations is given by
`((x_(1)+x_(2)+ ...+x_(15))+(3+4+5))/(18)`
`=((256-16)+(3+4+5))/(18)=(252)/(18) rArr 14.`