The mean and standard deviation of six observations are 8 and 4, respectively. If each observation is multiplied by 3, find the new mean and new standard deviation of the resulting observations.


Let us assume the observations be x1, x2, x3, x4, x5 and x6

It is given in the question that,


Mean = 8 and Standard deviation = 4



Now, according to question if each observation is multiplied by 3 and the resulting observations are yi then, we have:


yi = 3xi





= 3 × 8


= 24


We know that,





Hence, from (i) and (ii) we have:




Now, by substituting the values of xi and in (ii) we have:





Therefore, standard deviation of new observation = = 12


3
1