The standard normal distribution is more than just a curve.
It's a fundamental tool in statistics.
I will explain the math behind it with examples.
Yesterday we compared normal and standard normal distribution.
You can have a look here:
twitter.com/levikul09/status/1637759645191401472?s=20
The standard normal distribution is a special normal distribution where the mean is 0 and the standard deviation is 1.
It is also called z-distribution.
More on z-score below 👇
Z-score tell you how far the value is from the mean.
The measurement of this distance is the standard deviation.
Positive z score means that the given value is greater than the mean.
Negative z score means that the given value is less than the mean.
Let's consider these two scenarios:
- Dataset A has values between 100-150
- Dataset B has values between 500-1000
(they both follow a normal distribution)
You want to compare them, but they are on different scales.
One remedy is to standardize the data.
To standardize the data you can convert the values into z-scores.
During this process, the mean becomes 0 and the standard deviation becomes 1.
Here is the formula to achieve this:
Why is standard normal distribution practical?
- To compare and analyze datasets that have different scales
- Estimate the probability of observations in a distribution falling above or below a given value
Want to learn more about the second point?
Come back tomorrow!