More about normal distributions
And here are some specific (and real) normal distributions:
|The age of women attending this seminar is affected by a variety of factors:
||blood pressure readings are affected by a variety of factors:
An ideal, or theoretical, normal distribution is symmetrical and shaped a bit like a bell (its also called a Bell Curve). Or course your data will never follow an ideal normal distribution exactly, but many datasets do approximate a normal distribution.
An amazing fact is that distributions that are exactly normal can be described by 2 parameters. These two parameters are:
- where the distribution is centered or, the value at the peak.
- how wide the distribution is or, how much variability there is in the thing you’re measuring.
The centre of the distribution is called the mean. Because normal distributions are symmetric we can simply find the peak, and determine its position on the horizontal axis (this is known as the x coordinate); that’s your mean. Here are the two distributions from above:
Its harder to measure how wide the distribution is. Very big or very small fish, very high or low blood pressures, and very old or young ages do occur, at least with a small probability. So instead of measuring the entire width, we determine where the middle two-thirds of the data lies (actually the middle 68%, for reasons of mathematical theory). This measure is called the Standard Deviation, or SD. Again, the distributions from above:
So,68% of the observations fall between plus and minus 1 SD. Another way of saying this is that if you measure plus and minus 1 SD from the mean, you will shade 68% of the area under the curve. Most of us are not very good at eye-balling 68% of a curvy shape,
and there is a mathematical formula for determining the standard deviation. If you already
know it, good for you. If not, we’ll discuss it later. For now, just remember that
the standard deviation (SD) measures how far in each direction you have to go FROM THE MEAN along the x-axis to encompass 68%
of the population in other words, the SD measures how variable the population is.