Question

Flip N coins using a random number generator, and count the observed number of heads. Repeat M times, and compute the average, max, min, and standard deviation for the observed numbers of heads. Tabulate results. Do this for at least N = {10, 100, 1000} but also higher if you can, and one value of M (at least 30 but 10^4 or more if you can). To flip a coin in Excel, for example, CEILING(RAND()-0.5,1) returns 0=tail and 1=head with equal probability.

Answer 1

The number of tosses and it's descriptive statistics are given below:

Number of Tosses

N=10	N=100	N=1000
4	54	487
5	47	491
6	48	494
5	62	495
4	50	509
6	51	490
3	47	524
5	60	519
8	46	485
7	55	501
4	48	495
5	54	491
6	53	469
5	48	513
4	51	497
5	44	481
6	51	515
5	46	468
6	57	516
4	53	487
5	59	514
8	51	472
6	45	483
7	49	505
7	49	504
3	51	523
7	42	502
7	49	508
6	51	481
4	60	539
7	51	547
6	44	499
6	50	509
2	56	506
4	62	505
2	51	509
6	55	487
6	59	506
5	54	499
6	50	491
5	44	512
5	55	492

Descriptive statistics

	N=10	N=100	N=1000
Mean	5.30952380952381	51.4761904761905	500.476190476191
Standard Error	0.219512963268878	0.782531476242467	2.60019611858346
Mode	6	51	487
Median	5	51	500
First Quartile	4.25	48	490.25
Third Quartile	6	54.75	509
Variance	2.02380952380952	25.718931475029	283.962833914053
Standard Deviation	1.42260659488473	5.07138358586974	16.851196809546
Kurtosis	0.035358777436587	-0.423634004567769	0.655278968140574
Skewness	-0.367321369019064	0.354028902607459	0.426269788209806
Range	6	20	79
Minimum	2	42	468
Maximum	8	62	547
Sum	223	2162	21020
Count	42	42	42