Normal

What is normal? We use the word all the time, and we use it to define ourselves and our world.

We use the word as a way to calibrate ourselves, but do we really know what it is? We think we do, but do we?

"That is not normal."

"Can't you just act normal."

But, what is normal?

Well, defining normal is not as easy as one might think. It is that which is "according with, constituting, or not deviating from a norm, rule, or principle."

It is also "conforming to a type, standard, or regular pattern." It is also to be considered sane or that which occurs naturally. Definitions depend on the discipline. Normal is, for the most part, defined by a norm used as a standard, which implies that normal can change as the norm or standard changes.  We only need to examine standard deviation to make this point.

For our purposes today, normal is defined as normal distribution as graphed in your typical bell curve above. We define normal according to the bell curves for the following reasons:
                                        1. there is symmetry at the center
                                        2. 50% of the values are less and more than the mean  
                                        3. mean = mode = median

Through a bell curve, one can find the standard deviation. When standard deviation is calculated in accord with the bell curve one can expect the following situations:
                                        1. 68% of the values will fall within one standard deviations of the norm
                                        2. 95% of the values will fall within two standard deviations of the norm 
                                        3. 99.7% of the values will fall within three standard deviations of the norm

The number of standard deviations from the mean is called the standard score or the z score. To calculate a z score you must first subtract your value from the mean then divide by the standard deviation. This will give you a value that can then predicted outcome. 

For example, if you get a variable of .057 for your z score you can go to the standard deviation table, which has an x and y axis and chart your variable by looking up the .05 on the x axis then find .07 on the y axis. This will give you a value of 0.2157. This is converted to 21.57%, which is the expected outcome of success. 

Back to the idea of normal, normal depends on your predetermined standards. As an educator, I like to see the distribution of grades in accordance with the standard deviations of the bell curves. I like to see 68% of the grades within one standard deviation of the norm, 95% within two standard deviations of the norm and 98% within three standard deviations of the norm. But, the norm changes with each test because each test declares a new norm. 

Normal is not a fixed standard that is always tried and true. That which is normal today was not normal yesterday and will not be normal tomorrow. So, the next time someone says, "That's not normal." Ask them what there standard for normal is.