Question

If a valid of a variable X are X1, X2......... Xn then the variance of aX1, aX2....... aXn

Answer 1

Answer with explanation:

The set of variables  X are $X_{1},X_{2},X_{3},...........X_{n}$

now, these set of variables are multiplied by a, then

The set of new Variables are $a X_{1},a X_{2},a X_{3},...........a X_{n}$

Suppose the original set of values have variance = M

The variance is calculated by,

1. find the mean of data set.

2. get the modulus value of difference of mean and each value of data set.

3. Find the square of each new value obtained in data set.

4. Find the mean, of the new data set, and obtain it's square root.

This is way to calculate Variance.

So, when all the values in data set is multiplied by a, the the variance of new data set is = a × Variance of Original data set

           = a × M

           = M a