Obtaining Standard Normal Distribution Step-By-Step Guide in 2020
The word standardization may sound a little weird at first but understanding it in the context of statistics is not brain surgery. It is something that has to do with distributions. In fact, every distribution can be standardized. Say the mean and the variance of a variable are mu and sigma squared respectively. Standardization is the process of transforming a variable to one with a mean of 0 and a standard deviation of 1. You can see how everything is denoted below along with the formula that allows us to standardize a distribution.You may be wondering how the standardization goes down here. Well, all we need to do is simply shift the mean by mu, and the standard deviation by sigma.We use the letter Z to denote it. As we already mentioned, its mean is 0 and its standard deviation: 1.The standardized variable is called a z-score. It is equal to the original variable, minus its mean, divided by its standard deviation.Its mean is 3 and its standard deviation: 1.22. Now, let’s subtract the mean from all data points. As shown below, we get a new data set of: -2, -1, -1, 0, 0, 0, 1, 1, and 2.The new mean is 0, exactly as we anticipated.Showing that on a graph, we have shifted the curve to the left, while preserving its shape.Important: Adding and subtracting values to all data points does not change the standard deviation. Now, let’s divide each data point by 1.22. As you can see in the picture below, we get: -1.6, -0.82, -0.82, 0, 0, 0, 0.82, 0.82, and 1.63.If we calculate the standard deviation of this new data set, we will get 1. And the mean is still 0!In terms of the curve, we kept it at the same position, but reshaped it a bit, as shown below.