The normal distribution

The normal distribution is a probability distribution that has the well-known bell curve shape. While earlier pages have focused primarily on proportional data and frequency counts, many powerful methods (covered in subsequent pages) depend on probability distributions such as the normal distribution.

 
 
The classic 'bell-shaped' curve is central to how we do much of statistics because it is a widespread distribution in biology.
 

Normal Distribution

The Normal Distribution is probably one of the most commonly used statistical distributions. The reason it is so commonly used is because the Central Limit Theorem leads to many variables being normally distributed because they are caused by underlying processes that are additive. Watch the video to learn more!

Additional Resources

Whitlock & Schluter - The Analysis of Biological Data

Chapter 10: pages 273-292 [Sapling]

Great online visualisation by Whitlock & Schluter on the Central Limit Theorem

 

The normal distribution

Intro: Learn about the normal distribution, how the value of the mean and standard deviation affect it, and the 68-95-99.7 rule.

 

Central limit theorem

Intermediate: Explanation of what the central limit theorem is, and why it is useful.

 

Review Questions

 

  1. If we sample a normally distributed population, how will the mean of the samples themselves be distributed?

  2. If we sample a non-normal population, how will the mean of the samples be distributed?

  3. The number of vehicles leaving a highway exit over a 30 minute period during rush hour is approximately normally distributed with a mean of 500 vehicles and a standard deviation of 75 vehicles. If pnorm(450,500,75) = 0.25, what is the probability that over a randomly selected time period, there are more than 450 vehicles leaving the ramp?

The Next Steps

Confused?

Let’s move down the tree and review these concepts.

Ready to Move Forward?

Let’s move up the tree to the next topic.