1. # Heads or Tails?

## Draw conclusions

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In "Heads or tails?" Attended more than 100 people, so it's time to take stock.

Our main task in this project was to calculate the relative frequency of heads when tossing a coin. We remind you - to do this, it was necessary to divide the number of heads on the total number of tests carried out, ie, flipping a coin.

As we can see, the results of different participants have been very different: someone turned out very small values ​​of the relative frequency - from 0.2, and someone relative frequency was found to be 1, ie, the coin fell out every time up eagle ! (More units relative frequency can not receive, because you can not throw an eagle more times than was just throws).

Let's look at the histogram, which shows the distribution of the obtained values ​​of relative frequency of the number of participants, and find out what kind of values ​​are the most common.

Peak of the distribution is in the range of the relative frequency very close to 0.5. More accurate calculations give a value of the relative frequency w 0,492 ± 0,009.

As we can see, the most common frequency of heads coincides with the theoretically calculated probability equal to 0.5, with very high accuracy, although individually participants obtained results are very different! This is a very important finding, because it illustrates the statistical principle: the more tests will be carried out, the better the result will be what is expected (calculated theoretically).

So, our experiment confirmed: the large number of tests carried out the relative frequency of heads approaches the value of the probability equal to 0.5.

As for the hypothesis of the existence of the world's currency, in violation statistics, it has been neither confirmed nor refuted. Coin with a clear deviation from the norm can not be found, which, however, does not mean that such a coin does not exist, but only says that we do not have enough statistics to find it. To identify such a coin, if it exists in the world, you need to spend a much larger study, which would be carried out on a series of experiments with each of the world's currencies. Spend such a large experiment will, of course, very difficult. However, nothing is impossible!

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