Question

The mean of a data set comprising of $\text{16}$ observations is $\text{16}$ . If one of the observation valued $\text{16}$ is deleted and three new observations valued $\text{3, 4}$ and $\text{5}$ are added to the data, then the mean of the resultant data is

• A. $\text{14.0}$
• B. $\text{16.8}$
• C. $\text{16.0}$
• D. $\text{15.8}$

Answer 1

Answer: (A)

Given, $\frac{(\sum _{i=1}^{15}{x}_i)+16}{16}=16$
$\Rightarrow$ $\sum _{i=1}^{15}{x}_i$ $+16=\text{256}$
$\sum _{i=1}^{15}{x}_i=240$
Required mean $=\frac{\sum _{i=1}^{15}{x}_i+3+4+5}{18}=\frac{240+3+4+5}{18}$
$=\frac{\text{252}}{\text{18}}=\text{14}$