Given, The mean is 8 and SD is 4 for 6 observation

To Find: Find a new mean and new standard Deviation.

Formula Used: Standard Deviation ()

Explanation:

Let Assume, x₁,x₂,x₃,…,x₆ be the given observations.

So, Variance (X) = 8 (Given)

n=6

and (SD)

X =

Now, Let u₁,u₂,…u₂₀ be the new observation,

When we multiply the new observation by 3, then

U_i=3x_i (for i=1,2,3…,6) ……(i)

Now,

3×8 = 25

U = 24

Therefore, The Mean of new observation is 24

Now,

Standard Deviation

Since, Variance (X) =16

Variance (U) =

9×16

Hence, The mean of new observation is 24 and Standard deviation of new data is 12.