Dunder Methods

Dunder or magic methods in Python are the methods having two prefix and suffix underscores in the method name. Dunder here means “Double Under (Underscores)”. These are commonly used for operator overloading. Few examples for magic methods are: **init, add, len, repr etc.The init method for initialization is invoked without any call, when an instance of a class is created, like constructors in certain other programming languages such as C++, Java, C#, PHP etc. These methods are the reason we can add two strings with ‘+’ operator without any explicit typecasting.**

if __name__ == '__main__':

What is probability?

At the most basic level, probability seeks to answer the question, “What is the chance of an event happening?” An event is some outcome of interest. To calculate the chance of an event happening, we also need to consider all the other events that can occur. The quintessential representation of probability is the humble coin toss

The data and the distribution

The most important qualities to notice about the normal distribution is its symmetry and its shape. We’ve been calling it a distribution, but what exactly is being distributed? It depends on the context. In probability, the normal distribution is a particular distribution of the probability across all of the events. The x-axis takes on the values of events we want to know the probability of. The y-axis is the probability associated with each event, from 0 to 1

In a probability context, the high point in a normal distribution represents the event with the highest probability of occurring. As you get farther away from this event on either side, the probability drops rapidly, forming that familiar bell-shape. The high point in a statistical context actually represents the mean. As in probability, as you get farther from the mean, you rapidly drop off in frequency. That is to say, extremely high and low deviations from the mean are present but exceedingly rare.

Three Sigma Rule

The Three Sigma rule, also known as the empirical rule or 68-95-99.7 rule, is an expression of how many of our observations fall within a certain distance of the mean. Remember that the standard deviation (a.k.a. “sigma”) is the average distance an observation in the data set is from the mean. The Three Sigma rule dictates that given a normal distribution, 68% of your observations will fall between one standard deviation of the mean. 95% will fall within two, and 99.7% will fall within three. A lot of complicated math goes into the derivation of these values, and as such, is out of the scope of this article. The key takeaway is to know that the Three Sigma Rule enables us to know how much data is contained under different intervals of a normal distribution

Z-score

The Z-score is a simple calculation that answers the question, “Given a data point, how many standard deviations is it away from the mean?” The equation below is the Z-score equation.

Conclusion

We started with descriptive statistics and then connected them to probability. From probability, we developed a way to quantatively show if two groups come from the same distribution. In this case, we compared two wine recommendations and found that they most likely do not come from the same score distribution. In other words, one wine type is most likely better than the other one. Statistics doesn’t have to be a field relegated to just statisticians. As a data scientist, having an intuitive understanding on common statistical measures represent will give you an edge on developing your own theories and the ability to subsequently test these theories. We barely scratched the surface of inferential statistics here, but the same general ideas here will help guide your intuition in your statistical journey. Our article discussed the advantages of the normal distribution, but statisticians have also developed techniques to adjust for distributions that aren’t normal.