Question

If the algebraic sum of deviations of $20$ observations from $30$ is $20,$ then the mean of the observation is

• A. $30$
• B. $30.1$
• C. $29$
• D. $31$

Answer 1

Answer: (D)

We know that mean of the observations $=A+\frac{\sum f_i{d}_i}{\sum f_i}$ , 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,
$A=30,\sum f_i{d}_i=20\&\sum f_i=20$ . (given)
So, mean of the observations $=A+\frac{\sum f_i{d}_i}{\sum f_i}=30+\frac{20}{20}=31$ .