First get the average passing yards:
(3,832 + 3,779 + 3,655 + 3,642 + 3,579) / 5 = 3,697.4
Now get the squared residuals for each quarterback's passing yards. That is, compute the difference between each data and the average, then square the result. For example,
(3,832 - 3,697.4)^2 = 134.6^2 = 18,117.2
For the others, you should get squared residuals of
6,658.56
1,797.76
3,069.16
14,018.6
Take the sum of the squared residuals, then - since this is a sample, and not a population of all quarterbacks - divide the sum by 5 - 1 = 4 to get the variance:
(18,117.2 + 6,658.56 + 1,797.76 + 3,069.16 + 14,018.6)/4 = 10,915.3
The standard deviation is just the square root of the variance:
√(10,915.3) ≈ 104.48