The linear relation between the means is 100/4.5=200/9 and between the variances is 100/2.1=47.62 approx.
The first dataset is represented by 4.5±√2.1=4.5±1.45 approx.
The second dataset is represented by 100±√100=100±10.
If X is a datum in the first data set, it can be represented by a displacement from the mean: X=x+4.5.
To transform this X into the datum Y of the second data set we have Y=x√(100/2.1)+100≃6.9x+100=6.9(X-4.5)+100=6.9X-31.05+100=6.9X+68.95 approx.
ILLUSTRATION
Let’s choose a small dataset as an example of the first dataset. It has two elements: 4.5-√2.1 and 4.5+√2.1, that is, 3.05 and 5.95 roughly. The square root of the variance is the standard deviation.
The mean is 4.5 and the variance is 2.1.
Now, to perform the transformation we subtract the mean from the data: -1.45, 1.45.
We multiply these by 6.9: -10, 10 and then we add 100: 90, 110. This is the second dataset.
So X➝(X-4.5)6.9+100, which is the same as X➝6.9X+68.95.