00:01
In this problem, we are essentially doing computations and calculations, finding averages, and standard deviations.
00:10
Now, i know that this might seem like it's not very related to quantum mechanics, but this is essential math that you will need to know when you get to more advanced topics in quantum mechanics.
00:22
So for part a, the first thing that we know is from the data we're given, is that the average of j squared equals 21 squared, which is 441.
00:33
Now what we need to do is we need to find the average of j squared, and notice where our squared is because that's going to make a difference in our computation.
00:44
Well, this is going to be equal to 1 over n times the sum of j squared of n of j.
00:50
So this is a very simple summation calculation that we can do.
00:55
So this is going to be equal to 1 over 14 times this entire quantity.
01:01
14 squared plus 15 squared plus 3 times 16 squared plus 2 times 22 squared, plus 2 times 24 squared, plus 5 times 25 squared squared.
01:12
Now all you have to do is plug that into a calculator, and we're going to find that our j squared average is 459 .57.
01:22
And now for part b, we need to find the standard deviation.
01:26
Luckily for us, we don't have too much data where we can do this by hand.
01:31
So let's just make a quick table of what we're doing.
01:34
We have j and we have delta j.
01:36
J is going to be equal to 14, 15, 16, 22, 24, 25.
01:43
Delta j is negative 7, negative 6, negative 5, 1, 3, and 4.
01:49
Now what we can say is we know that 6 squared is equal to 1 over n times the sum of delta j squared times n of j...