Discussion Forum

The mean of the data set comprising of 16 observations in 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

Answer:

Explanation:

Given  ,  $\frac{x_{1}+x_{2}+x_{3}+...+x_{16}}{16}=16$

  $\Rightarrow$     $\sum_{i=1}^{16}x_{1}=16\times16$

 Sum of new observations

           $=\sum_{i=1}^{18}y_{i}=(16\times16-16)+(3+4+5)=252$

  Number of observations =18

$\therefore$    New mean  =   $  \frac{\sum_{i=1}^{18}y_{i}}{18}=\frac{252}{18}=14$