The most important distribution in all of statistics is the normal distribution.
The reason for its importance is that many measures of human individual
differences naturally fall into this normal or bell-shaped curve. Therefore,
many of the statistics that we will use assume that the underlying population
that we are sampling is normally distributed. When we create a histogram,
if the scores are normally distributed, we could overlay a picture of a normal
curve on them. Of course the curve that I am showing you is an idealized shape,
this is how the data should look in the real world. Of course they don't always
look like this in the real world. In fact, they will probably never look like this,
and yet the more that we learn about human measurement the more often we see
things that approach this normal curve. Whether we are measuring height, weight
IQ, guesses made by a crowd, or level of job satisfaction, many human measurements
with enough people begin to look like this normal curve. For instance, notice
the wear pattern on the panic bar of a door in a public place. Doors and public
places have to open outward so they have a bar that runs the width of the door
it's called a panic bar, because you can open the door simply by pressing on it
if you were in a panic running out of the building because the building was on
fire. So obviously the panic bar can be helpful in an emergency. On double doors,
most people tend to touch the panic bar on the edge farthest from the hinges
that would be the middle of a double door. Look at the amount of wear on the
handles, and you will see that the wear pattern is shaped like a normal curve.
There are greater amounts of touching in the middle, and less as you go to the
extremes. Begin to look around in the human world, and you will see the normal
curve appearing with great regularity. Because it is so important there are
some things that we will need to know about the normal curve. First, the normal
curve is used with interval or ratio level data, what
we will call scale data. There is an x and y axis but the y axis is typically not
included, it's just understood to be there, but the y axis still represents
frequency. If you recall the rope that we left lying on the football field, in the
rows where there were more people (greater frequency) the rope was further
from the sideline. In this analogy, we could think of the end zone as the y
axis. The y axis will not normally be labeled it is simply understood that
higher means more. The curve in a normal distribution is a smooth continuous line,
and because this is an idealized form, all of the measures of central tendency
converge on the mean. The median and the mode will be the same number as the mean.
This will be useful when we learn about central tendency. We can determine how
closely a distribution matches normality by studying the mean, median, and mode.
Normal curves are symmetrical, which means that they are divided right down
the middle. The left half and the right half look the same. If I print the normal
curve on a piece of paper, and then fold that paper right down the middle, the
left and right halves of the normal curve will match perfectly. The most
frequently occurring scores will be in the middle part of the normal curve, where
the curve is furthest from the x-axis. Less frequently occurring scores are
further away from that middle score. In what we will call the tails of the curve.
Extreme scores way out on the end of the curve are called outliers. Think of
people who you know who are unusually tall or unusually short. How many super
tall or super short people do you know? Probably not very many. That is because
most people are not super tall or super short. Most people are in the middle near
the average. So the frequency of very tall people is less than the frequency
of average height people. If you know someone for instance who is seven feet
tall, then you know someone whose height is an outlier. In our example of the
football field, our outlier person was 6 feet 6 inches tall. When we are doing
data analysis we will need to decide what to do with those outliers scores,
and we'll learn more about that in another chapter.