Make this list:

i  xi
---------------
1  65
2  88
3  83
4  80
5  78
6  90

Find the mean (the average of those 6 number which is 80 2/3

Then you subtract the mean, x̄ = 80 2/3 from each one, and put them in a list
out to the right:

i  xi    xi-x̄
---------------
1  65  -15 2/3
2  88    7 1/3
3  83    2 1/3
4  80   -  2/3  
5  78   -2 2/3
6  90    9 1/3
--------------

Then you square each number in that list and put them in a list out to the
right:

i  xi    xi-x̄    (xi-x̄)²
------------------------
1  65  -15 2/3   245 4/9
2  88    7 1/3    53 7/9
3  83    2 1/3     5 4/9
4  80   -  2/3       4/9
5  78   -2 2/3     7 1/9
6  90    9 1/3    87 1/9
-------------------------
  484    0       399 1/3  
   ÷              ÷
   6              5 <--divide by 1 less than the number of numbers.
   =              = 
80 2/3           79 13/15
   =              =
   x̄             σ² = the variance of the sample

To get the standard deviation, we take the square root of the variance:

                  <--standard deviation

Edwin