 # Normal Distribution

Normal Distribution:

The normal distribution is a probability density which is bell-shaped, symmetrical, and single peaked. The mean, median and mode coincide and lie at the center of the distribution. The two tails extend indefinitely and never touch the x-axis (asymptotic to the x-axis). A normal distribution is fully specified by two parameters – mean and the standard deviation.
A Standard Normal Distribution is one that has zero mean, and standard deviation of 1. Data that are standardized (subtract the mean, divide by the standard deviation) are often compared to the Standard Normal distribution, to see where an individual observation lies relative to it. The formula for the Standard Normal probability density function (PDF) is
For a finite population of size N, where μ is population mean,
σ^2=1/N ∑_(i=1)^N▒(x_i-μ)^2 , or
If X is a random variable with mean μ,
σ^2=E[(X-μ)^2 ].

Browse Other Glossary Entries

## Test Yourself

Planning on taking an introductory statistics course, but not sure if you need to start at the beginning? Review the course description for each of our introductory statistics courses and estimate which best matches your level, then take the self test for that course. If you get all or almost all the questions correct, move on and take the next test.

### Data Analytics

Considering becoming adata scientist, customer analyst or our data science certificate program?

Analytics Quiz

Statistics Quiz

### Statistics

Looking at statistics for graduate programs or to enhance your foundational knowledge?

Statistics 1 Quiz

Regression Quiz

Regression Quiz

### Biostatistics

Entering the biostatistics field? Test your skill here.

Biostatistics Quiz

Statistics 2 Quiz

### Stay Informed

Our Blog

Read up on our latest blogs

Certificates

Courses

Find the right course for you