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Grokking Data Science

## 4. Normal Distribution (Gaussian)
A normal distribution, the bell curve or Gaussian Distribution, is a distribution that represents the behavior in most situations. For example, exams scores are typically a bell curve where most students get the average score, C, a small number of students scores a B or a D, and an even smaller number scores an F or an A. This results in a distribution that looks like a bell:



The bell curve is symmetrical, half of the data will fall to the left of the mean value and half will fall to the right of it.

Many things follow this type of spread, this is why this is used most often; you'd seen anywhere from businesses to academia to government. Here are some examples to give an idea of the variety covered by normal distributions:
- Heights of people
- Blood pressure
- IQ scores
- Salaries
- Size of objects produced by machines

Some facts to remember about what percentage of our data falls within a certain number of standard deviations from the mean:
- **68%** of values are within 1 standard deviation of the mean
- **95%** of values are within 2 standard deviations of the mean
- **99.7%** of values are within 3 standard deviations of the mean




***Why is it good to know standard deviations from the mean?***

Because we can say the likelihood with which any value is:
- likely to be within 1 standard deviation (68 out of 100 cases)
- very likely to be within 2 standard deviations (95 out of 100 cases)
- almost certainly within 3 standard deviations (~99 out of 100 cases)

The number of standard deviations from the mean is also called the **standard score** or **z-score**. Z-scores are a way to compare results from a test to a “normal” population. 

Say we are looking at a survey about heights. A z-score can tell us where a person’s height is compared to the average population’s mean height. A score of zero tells us that the value exactly matches the average, while a score of +3 tells us that the value is much higher than average.

The mean and variance of a random variable, *X*, which is said to be normally distributed is given by:

$$Mean = E(X) = \mu$$

$$Variance = V(X) = \sigma^2$$ 

where µ is the mean value and σ the standard deviation.

The z-score is then given by:

$$z = \frac{x-\mu}{\sigma}$$



# 4. Normal Distribution (Gaussian)
A normal distribution, the bell curve or Gaussian Distribution, is a distribution that represents the behavior in most situations. For example, exams scores are typically a bell curve where most students get the average score, C, a small number of students scores a B or a D, and an even smaller number scores an F or an A. This results in a distribution that looks like a bell:



Python Fundamentals for Data Science

The Fundamentals of Statistics

Machine Learning 101

End-to-End Machine Learning Project

The Real Talk

Types of Distributions - Normal

4. Normal Distribution (Gaussian)