The Median and variance of a distribution are 35 &2.56 respectively. Find median & variance if all obsn*3?

Question

The Median and variance of a distribution are 35 &2.56 respectively. Find median & variance if each observation is multiplied by 3.

Answer 1

The median scales with the data

Median = 35*3 = 105

The variance scales with the square of the data:

Variance = 2.56*9 = 23.04

Answer 2

Since all observations are being multiplied by 3 the median would just be the original median times 3, that's

35 times 3 = 105

The variance is 2.56 of the original observations so the

variance of the new distribution would just be 3² x 2.56

which is  23.04