Standard deviation? COIN TOSS HELP

[aisha]

Standard deviation? COIN TOSS HELP!

I tossed a coin 20, 30 and 50 times are recorded number of heads and tails and to get the deviation I first subtracted the expected from the observed for both heads and tails then I squared this value and divided it by the number of events and then toook the square root of this final value to get the standard deviation, its all in a chart and tells you what to do step by step.

for 20 tosses = 0.70 standard deviation
30 tosses=0.70 standard deviation
50 tosses = 1.41 standard deviation

The question says compare the standard deviations from the expected 20, 30, 50 tosses, what seems to be the relationship between the sample size and the standard deviation?

I think as the sample size gets bigger the standard deviation also increases, I am not sure can someone please help me out please.

 

[BobG]

You didn't follow the directions very well . I wouldn't consider myself an expert on probability - I've generally relied on software and have a general feel for the significance of the result, but, using a little reverse engineering from the directons:

.70 squared is .5.

.5 times 20 is 10.

So you probably expected to get about 10 heads. The difference between what you expected and what you actually got was 10? In other words, you threw 20 straight heads or 20 straight tails? (Unless of course, you expected to throw 20 straight heads or 19 out of 20 or some other 'interesting' guess). Being able to get 100 straight heads in 50 tosses is even more impressive .

If you wound up with, say, 15 heads in 20 tosses, that's 5 off of what you would have expected. Divide the 5 by 20, which gives you .25. Take the square root to get your standard deviation (about .5). That could mean that you expect your actual results to be within 50% of your expected results (5 is 50% of 10, right?). (The procedure looks a little lame when applied to coin tosses, but it's simplicity makes it easy to see what you're actually doing).

In general, your standard deviation should go down as the number of samples goes up. Your maximum deviation would be when every single toss resulted in the same - all heads or all tails. Your chances of that happening go down as the number of samples increases.

 

[aisha]

.70 squared is .5.

.5 times 20 is 10

I don't understand why did you do this? How come my data is off... hmm well the number of events is 2 right?

 

[cepheid]

.70 squared is .5.

.5 times 20 is 10

I don't understand why did you do this? How come my data is off... hmm well the number of events is 2 right?

An event is a coin toss. The number of events could be 20, 30, or 50, but I really don't see how it could be 2. Could you post a sample calculation?

 

[aisha]

What do u means sample calculation? I thought the event was 2 because there are two possible events when you toss a coin? You can either get heads, or tails.

 

[BobG]

.70 squared is .5.

.5 times 20 is 10

I don't understand why did you do this? How come my data is off... hmm well the number of events is 2 right?

I tried to figure out how many heads and tails you received from your standard deviation. In other words, I started from the end and worked through your directions backwards.

As cepheid said, there are 20 events, 30 events, and 50 events. Each event has two possible outcomes - heads or tails.

It would help to know how many heads you got out of 20 tosses, how many for 30 tosses, and how many for 50 tosses. Otherwise, we have to resort to half-baked procedures like mine to try to guess what your raw results were.

 

[aisha]

20 tosses
observed 11 heads 9 tails
expected 10 heads 10 tails
Deviation 1 and -1

30 tosses
observed 16 heads 14 tails
expected 15 heads 15 tails
Deviation 1 and -1

50 tosses
observed 23 heads 27 tails
expected 25 heads 25 tails
Deviation -2 and 2

in the second table I had to take the deviation from table 1(above) and square it then in the second column I had to take the squared value and divide by the number of events (this is where I think I went wrong I only divided by two thinking the number of events was heads or tails) then the last column in the table says take the square root of the previous column.

That is it!