# Statistical variation of a flipped coin

1. Nov 28, 2007

### SciSteve

I found a statistics question and am wondering how its figured out, the way its worded is hard to understand what everything means. anyhow..

If a coin is flipped N times, one expects to get "heads" roughly half the time. More precisely, Number of heads=N/2+Δn where Δn is the statistical variation. Typically, one expects Δn/N≈1/2√N
thats 2 multiplied by square root of N in denominator, and the question proceeds...
You sometimes see a news report of a pole asking who would be the best president. The report typically says that if two candidates' numbers differ by less than 3%, then it is a "statistical dead heat." If this means the difference is less than would be expected from the statistical variation, how many people were asked the question?

Any help with some explanation would be greatly appreciated thanks in advance.

2. Nov 29, 2007

### uart

What level and course are you doing Steve?

One part of the question is pretty loosley worded and makes me think it might be aimed at someone who has only basic knowlegde of statistics.

The statement "Typically, one expects Δn/N≈1/2√N" is not quite correct as the variation can be either positive or negative and the expected value is exactly zero ("expected value" has a definite menaing in statistics). It's actually the standard deviation (stdev) that is equal to sqrt(N)/2 and therefore stdev/N = 1/(2 sqrt(N)).

Anyway that aside, the question is basically just asking you this. For what value of N is sqrt(N)/2 equal to 3% of N. Hopefully you can make an equation out of that and solve for N.

3. Nov 29, 2007

### SciSteve

its actually for an intro level physics course, and I've never took statistics so this stuff kinda confuses me.