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.

Answer

Mean is `8`

Standard deviation is `12`

Explanation

Let the observations be`{x}_{1}, {x}_{2}, {x}_{3}, {x}_{4}, {x}_{5}, and {x}_{6}`

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



`Rightarrow ``{ Mean }={x}=frac{{x}_{1}+{x}_{2}+{x}_{3}+{x}_{4}+{x}_{5}+{x}_{6}}{6}=8`...(i)


If each observation is multiplied by 3 and the resulting observation are `{y}_{i}`, then

`{y}_{i}=3 {x}_{{i}}, text { for } {i}=1 `to` 6`


...