Law of large numbersCoin flip trial Coin flip trial 2 1 1 1 0 0 1 1 0 0 1 1 1 0 0 0 0 1 1 1 0 1 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 0 1 1 1 1 1 1 0 0 0 0 1...

Hello, can some one help with a probability question?

I have been provided with 2 samples for coin flips where heads =1, and tails = 0. The first sample contains 2 trials, and the second sample contains 10 trials. The Mean for the first sample was 0.54, and the mean for the second sample was 0.51...which can be explained by the Law of Large Numbers.

But where i find some trouble is explaning why the Standard Deviation is 0.50 in both cases....Does this have something to do with a binomial probability? I tried limiting the sample and the SD moved from 0.47, 0.45 to 0.50....