Correct option is: C) 28
Let \(x_1\)'s are observations of the original data .
Given that mean of data is 9.
Let total no. of observation be n.
\(\therefore\) Sum of observations = n\(\overline x\) = 9n
\(\Rightarrow\) \(\sum \limits _{i=1}^n x_i\) = 9n ....(1)
Since, each observation ( \(x_1\)'s) are multiplied by 3 and then 1 is added to each result.
\(\therefore\) (\(3x_i + 1\))'s are new observations.
\(\therefore\) Mean of formed data = \(\frac {sum\, of \,new \,observations}n\)
= \(\frac {\sum \limits_{i=1}^n (3x_i+1)}{n}\)
= \(\frac {\sum \limits_{i=1}^n 3x_i + \sum \limits_{i=1}^n 1}{n}\)
= \(\frac {3\sum \limits_{i=1}^n x_i +n}{n}\) (\(\because\) \(\sum \limits_{i=1}^n 1 = 1 + 1+1+...+1 (n \, times) = n\))
= \(\frac {3\times 9n+n}{n} \) (From (i))
= \(\frac {28n}{n} = 28\)
Hence, the mean of new observations is 28.