If each observation of data is increased by ‘a’ then mean is increases by…………

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.

Correct option is: A) a