Day 1 - Normal Distribution, Z-score, Standard Normal distribution - #66DaysofData Challenge

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By Jerin Lalichan 

1. Normal Distribution (Gaussian Distribution)

    How the data is distributed can tell us a lot about the data. There are over 20 different types of data distributions commonly used in data science to develop a  model. The normal distribution is one of the most common data distributions seen in nature, for example, the distribution of the heights of human beings. It is also called as Bell Curve.

Image credits: Statistics by Jim

Properties:

  • Parameters of a bell curve are :
  1. Mean - which determines the maximum height of the curve
  2. Standard deviation - which determines how wide should be the curve 
  • The mean, median, and mode are the same.
  • The distribution is symmetrical, in other words, the data points are symmetrically distributed around the mean value.


2. Z score

    It is a number that represents how far is, ie how many standard deviations away is a point located, measured from the mean value. So farther the point, greater will the z-score. It is also called  Standard score.

    It generally varies from -3 to 3, also points beyond the limit can be considered as unusual data.

3. Standard Normal Distribution

    It is also called Z-distribution. It is nothing but a special case of normal distribution. The x values in the normal distribution are transformed into corresponding z values using the above equation. This process is called standardization and the resulting distribution is called Standard Normal Distribution. 


Properties:

  • The value of mean (μ=0) = 0
  • The value of standard deviation (σ=1) = 1
  • It is a probability distribution, and the area under the curve gives you probability values.
  • Total area under the curve is 1 (100%)

4. Empirical rule - 68–95–99.7 Rule

Image credits: Statistics by Jim

    It is also called the 3 sigma rule. The empirical rule in statistics, also known as the 68-95-99 rule, states that for normal distributions, 68% of observed data points will lie inside one standard deviation of the mean, 95% will fall within two standard deviations, and 99.7% will occur within three standard deviations.


    I am doing a challenge - #66DaysofData  in which I will be learning something new from the Data Science field for 66 days, and I will be posting daily topics on my LinkedIn, On my GitHub repository, and on my blog as well.


Stay Curious!  




  

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