The 1st 2 stand deviations matches..........14i.........and the critical line at 1/2..................the highest point is half way through.................where m = 0.........zeros Dr. Riemann.............AND........68% and 95%.........the 1st 2.......like 1/2..................68 and 95............adding the single digit to the double digit........gives u 14.........like 14i............6 + 8 = 14............9 + 5 = 14...............9 + 9 = 18...........that one does not.............99.8% is the 3rd one..........but the 1st 2 do.........just like the line and the complex number......1/2 + 14i........that goes with the 1st zero.................the zenith is halfway through........1/2 way through................


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:

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).

It 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":

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!

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):

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