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 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