A little help with a simple SD question...?

I have a question to do with standard deviation.
If i flip a fair coin 100 times and the result is:
61heads
39 tails
As far as I remember to work out the standard deviation (please correct if Im wrong) is:
(50/100)x(50/100)=0.25
0.25x100= 25
squareroot x 25 = 5

So 1 standard deviation is 5. My resullt of 61 heads is just over 2 standard deviations from average.
If 95% of results fall within 2 Standard deviations of average, my question is:

Does the 95% refer to a single starting toss or groups of 100 tosses??

Thanks!!

Quote: Walkinshaw30t

Does the 95% refer to a single starting toss or groups of 100 tosses??

Thanks!!

Since you did this step:
0.25x100 = 25

It means about 95% of 100-toss sets will fall between 40 and 60 heads.

Just for clarification:

The famous 1 SD = 68% and 2 SD = 95% refers to the normal (Gaussian) distribution. Now, any event when repeated over a "large" number of times eventual follows a normal distribution (that is the law of large numbers). If 100 tosses is considered "large", then yes this 95% refers to groups of 100 tosses.

On the other hand, a single toss has SD = 0.25. But all results are either 0 or 1, and hence certainly not a normal distribution. So don't expect that 68% fall inbetween the 1 SD region 0.25 - 0.75 (in fact 0% fall in that range). Likewise 95% dont fall inbetween the 2 SD region 0 - 1 (in fact it is 100%). The reason for this is, "1" (the only toss) is simply not a "large" number.

Ok I though that was the case.
Thanks for clearing it up for me!