The mean of the data set comprising of 16 observations is 16. If one of the observations 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  

Let $x_1,x_2,x_3,\dots \dots ,x_{16}$ be 6  observations of the 

given data set. It is given that the mean of these

 observations is 16.  

$\begin{array}{r}\therefore \frac{x_1+x_2+x_3+\dots +x_{16}}{16}=16\\ \Rightarrow x_1+x_2+x_3+\dots +x_{16}=256\end{array}$

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

$\begin{array}{l}\frac{\left(x_1+x_2+\dots +x_{15}\right)+(3+4+5)}{18}\\ =\frac{(256-16)+(3+4+5)}{18}=\frac{252}{18}\Rightarrow 14.\end{array}$