Answer :

Let us assume the observations be x_{1}, x_{2}, x_{3}, x_{4}, x_{5} and x_{6}

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 y_{i} then, we have:

y_{i} = 3x_{i}

= 3 × 8

= 24

We know that,

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

Now, by substituting the values of x_{i} and in (ii) we have:

Therefore, standard deviation of new observation = = 12

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