Q. If the algebraic sum of deviations of $20$ observations from $30$ is $20,$ then the mean of the observation is
NTA AbhyasNTA Abhyas 2022
Solution:
We know that mean of the observations $=A+\frac{\displaystyle \sum f_{i} d_{i}}{\displaystyle \sum f_{i}}$ , where $A$ denotes the assumed mean and $f_{i}$ denotes the frequency of an observation and $d_{i}$ denotes the deviation of an observation from the assumed mean.
In our case,
$A=30,\displaystyle \sum f_{i}d_{i}=20\&\displaystyle \sum f_{i}=20$ . (given)
So, mean of the observations $=A+\frac{\displaystyle \sum f_{i} d_{i}}{\displaystyle \sum f_{i}}=30+\frac{20}{20}=31$ .
In our case,
$A=30,\displaystyle \sum f_{i}d_{i}=20\&\displaystyle \sum f_{i}=20$ . (given)
So, mean of the observations $=A+\frac{\displaystyle \sum f_{i} d_{i}}{\displaystyle \sum f_{i}}=30+\frac{20}{20}=31$ .