Normal Distribution

Normal Distribution

Data can be "distributed" (spread out) in different ways.
It can be spread out
more on the left		 
Or more on the right
data skewed left data skewed right
   
Or it can be all jumbled up
data random
But there are many cases where the data tends to be around a central value with no bias left or right, and it gets close to a "Normal Distribution" like this:
bell curve
A Normal Distribution
The "Bell Curve" is a Normal Distribution.
And the yellow histogram shows some data that
follows it closely, but not perfectly (which is usual).
bellIt is often called a "Bell Curve"
because it looks like a bell.
Many things closely follow a Normal Distribution:
  • heights of people
  • size of things produced by machines
  • errors in measurements
  • blood pressure
  • marks on a test
We say the data is "normally distributed":
normal distribution with mean median mode at center
The Normal Distribution has:
  • mean = median = mode
  • symmetry about the center
  • 50% of values less than the mean
    and 50% greater than the mean

Quincunx

You can see a normal distribution being created by random chance!
It is called the Quincunx and it is an amazing machine.
Have a play with it!		 quincunx

Standard Deviations

The Standard Deviation is a measure of how spread out numbers are (read that page for details on how to calculate it).
When we calculate the standard deviation we find that generally:
normal distrubution 68%, 95%, 99.7%
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

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