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

Question

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 (A) 14.0 (B) 16.8 (C) 16.0 (D) 15.8

Tardigrade Admin · Accepted Answer

Given, ((. displaystyle ∑ i = 115xi .) + 16/16) = 16 ⇒ displaystyle ∑ i = 115xi +16= text256 ⇒ displaystyle ∑ i = 115xi=240 Required mean =( displaystyle ∑ i = 115xi+3+4+5/18)=(240 + 3 + 4 + 5/18) =(252/18)=14

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

$14.0$

$16.8$

$16.0$

$15.8$

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

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

14.0

16.8

16.0

15.8