The rmsd for the 20-week period is the square root of one-twentieth of the sum
where the represent the individual readings, and is the amount by which the reading differs from the 20-week mean 1.5. But when you calculate the rmsd for the 52-week period, you are no longer using 1.5 as the mean, but 1.62. So in calculating the contribution of these readings to the 52-week rmsd, you need to use the sum
To get from (*) to (**), you have to take (*) and add the difference between (**) and (*), namely
When you multiply out the brackets and subtract, the terms cancel out and you are left with . But is 20 times the mean of the , namely . Using that, you should find that the sum (**) is equal to 0.488.
Now do exactly the same process to the 32-week period, and you should get the sum there to be 0.464.
Therefore the 52-week rmsd is