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  4. The mean of a data set comprising of 16 observations is 16 . If one of the observation value 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

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

NTA AbhyasNTA Abhyas 2022Statistics

Solution:

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