Question

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 added to the data, then the mean of the resultant data is

• A. 16.8
• B. 16.0
• C. 15.8
• D. 14.0

Answer 1

The correct option is D

14.0

Given, $\frac{x_1+x_2+x_3+\cdots +x_{16}}{16}=16$
$\Rightarrow {\sum }_{i=l}^{16}{x}_i=16\times 16$
Sum of new observations
$={\sum }_{i=l}^{18}{y}_i=(16\times 16-16)+(3+4+5)=252$
Number of observations = 18
$\therefore$ New mean $=\frac{{\sum }_{i=l}^{18}{y}_i}{18}=\frac{252}{18}=14$