Given:
The mean of a set of 6 integers is 30.
If one of the numbers is removed, then the new mean is 34.
To find:
The removed number.
Solution:
The formula for mean is
[tex]\text{Mean}=\dfrac{\text{Sum of observations}}{\text{Number of observations}}[/tex]
The mean of a set of 6 integers is 30.
[tex]30=\dfrac{\text{Sum of 6 observations}}{6}[/tex]
[tex]30\times 6=\text{Sum of 6 observations}[/tex]
[tex]180=\text{Sum of 6 observations}[/tex]
If one of the numbers is removed, then the mean of remaining 5 numbers is 34.
[tex]34=\dfrac{\text{Sum of 5 observations}}{5}[/tex]
[tex]34\times 5=\text{Sum of 5 observations}[/tex]
[tex]170=\text{Sum of 5 observations}[/tex]
Now,
Removed number = Sum of 6 observations - Sum of 5 observations
= 180 - 170
= 10
Therefore, the removed number is 10.
