Correct option is: A) a
Let \(x_1\) 's are original observations.
Let there be n No of observations
\(\therefore\) Sum of observations = \(n\overline x\)
\(\Rightarrow\) \(\sum \limits_{i=1}^n x_i \) = \(n\overline x\) ....(1)
If each observation of data is increased by a then (\(x_i+a\))'s are new observations of data.
Sum of new observations = \(\sum \limits _{i=1}^n (x_i+9) = \sum \limits _{i=1}^n x_i + a \sum \limits _{i=1}^n 1\)
= \(n\overline x\) + na
= n (\(\overline x\) + a)
\(\therefore\) Mean of new observations = \(\frac {sum}n = \frac {n(\overline x + a)}{n} = \overline x + a\)
Hence, if each observation of data is increased by a, then new mean is increases by a.
