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, $\frac{\left(\right. \displaystyle \sum _{i = 1}^{15}x_{i} \left.\right) + 16}{16} = 16$
$⇒ \, \, \, $ $\displaystyle \sum _{i = 1}^{15}x_{i}$ $+16=\text{256}$
$\displaystyle \sum _{i = 1}^{15}x_{i} = 240$
Required mean $= \frac{\displaystyle \sum _{i \, = \, 1}^{15}x_{i} + 3 + 4 + 5}{18} = \frac{240 + 3 + 4 + 5}{18}$
$ \, = \frac{\text{252}}{\text{18}} = \text{14}$