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.

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Solution

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

It is given that mean is 8 and standard deviation is 4.

If each observation is multiplied by 3 and the resulting observations are y_i, then

From (1) and (2), it can be observed that,

Substituting the values of x_i and in (2), we obtain

Therefore, variance of new observations =

Hence, the standard deviation of new observations is

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