Question

The standard deviation of 20 observation is root 6 if each observervation is mulitipied by 3 find the standard deviayion and variancescof the resuliting observation. Solve this an
swers

Answer 1

The standard deviation of 20 observation is root 6 if each observation is multiplied by 3, the standard deviation and variance of the resulting observation are respectively 3$\sqrt{6}$ and 54.

1) The formula for variance is V = σ² = $\frac{1}{20}$ * ( Xi - Xmean )²

2) Whenever the observation is multiplied by 3, the mean of the new set of numbers is 3 times the mean of the previous set.

3) So, the standard deviation will be 3 times the previous observation i.e. 3$\sqrt{6}$

4) Since, variance is the square of the standard deviation, the new variance will be 3² * 6 = 54