Question

If the variance of 1, 2, 3, 4, 5, ...., 10 is 99/12 then
the standard deviation of 3, 6, 9, 12, ...30 is

OPTIONS
A)297/4

B)3/2 ROOT33

C)3/2 ROOT 99

D) ROOT 99/2​

Answer 1

ROOT 99/2...

This is right gies......

Answer 2

Answer:

Correct option: C)  $\frac{3}{2}\sqrt{99}$.

Step-by-step explanation:

The statistical approach to determine the level of variation in a random set of data is to define this dataset's variance.

Consider that the variance of a random variable X is $\sigma^{2}$. Then the variance of the linear transformation of this random variable X will be:

$Var(aX)=a^{2}Var(X)=a^{2}\sigma^{2}$

It is provided that the variance of the set [1, 2, 3, 4, ..., 10] is,

$\sigma^2=\frac{99}{12}$

The new data set is [3, 6, 9, 12, ..., 30].

It can be observed that the new data set is 3 times the values of the first data set.

Following the concept of variance of a linear transformation, the variance of the new data set will be:

$\sigma^{2}_{new}=(3^{2})\times \sigma^{2}\\\\\sigma^{2}_{new}=9\times \frac{99}{12}\\\\\sigma^{2}_{new}=\frac{297}{4}$

Now compute the standard deviation of the new data set as follows:

$\sigma_{new}=\sqrt{\sigma^{2}_{new}}\\\\\sigma_{new}=\sqrt{\frac{297}{4}}\\\\\sigma_{new}=\frac{3}{2}\sqrt{99}$

Thus, the standard deviation of the new data set is $\frac{3}{2}\sqrt{99}$.

The correct option is C.