Correct option is: B) 19
Given that the mean of data is 10.
Let number of observations be n
\(\therefore\) Sum of original observations is \(\sum x_i = 10n\) ...(1)
Given that each observation (\(x_i\)) is multiplied by 2 and 1 is subtracted from each result.
\(\therefore\) New observations are of type (2\(x_i\)-1).
Sum of new observations = \(\sum\) (2\(x_i\)-1).
= 2\(\sum\)\(x_i\) -\(\sum\) 1
= 20n - n (\(\because\) \(\sum\)\(x_i\) = 10n & \(\sum\) 1 = n)
= 19 n
\(\therefore\) Mean of new observations = \(\frac {sum \, of \, new\,observations}{ number \, of\, observations}\)
= \(\frac {19n}{n} = 19\)
Hence, the mean of new observations is 19.