Introduction to a variety of useful statistical ideas and techniques - Improving the User Experience through Practical Data Analytics - page 2

µ = 160 162 163.7 etc.

FIGURE 1.1
A family of normal curves.

is symmetric around this center point (i.e., the left and right sides of the curve are mirror
images of one another) a fact that allows us to more easily interpret other points within
the curve. This center point is always denoted by the Greek letter, μ, which is referred to
as the “Greek m.” In English-language countries, it's usually pronounced “myu.”
The key interpretation of a normal curve (or even a curve with a different shape) is
that the area under the curve between any two points on the horizontal x axis equals
the probability of getting a result in between these two points. So, inding the area
under a normal curve between two points is the same as inding the probability that
you will get a result between two points. This notion holds true for all kinds of data,
including all kinds of UX metrics like task completion times and satisfaction ratings.
A normal curve is determined not only by its center, but also by how tall and
thin or short and fat the curve is. The area under the curve must always equal 1—
although we don't specify the units of the “1.” This means, essentially, that 100%
of the data possibilities are represented under the curve. But a normal curve has the
same area being taller and thinner or shorter and fatter. An analogy is that a man
weighs 160 pounds, but can still be either tall and thin, or short and fat, or any inter-
mediate combination. Of course, to keep a constant area of 1, any curve that is taller
must be thinner and, if shorter, must be fatter.
This lexibility of a normal curve is very useful for a number of reasons. First, if a
curve is relatively taller and thinner, it represents a situation where there is relatively
little variability in the result that comes out—nearly all of the area is near the center.
On the other hand, if the curve is relatively shorter and fatter, it represents a situation
where there is relatively more variability—more of the area is farther away from the
center. In responding to a Likert-scale question, larger variability would represent
the fact that there is less agreement among the respondents (whether the pattern of
responses was bell-shaped or not).
Second, different phenomena have more variability than other phenomena, but
the normal curve can accommodate these differences. For example, the time it takes
to perform certain usability test tasks will vary from person to person to a different
extent from task to task. But the normal curve has the lexibility to accommodate all
the different degrees of variability.
Traditionally, we measure how tall and thin or short and fat a normal curve is by a
quantity called the “standard deviation.” Don't let the term intimidate you. It's similar
to, but not exactly the same as, measuring the average distance of all your data points
from the mean. It's always denoted by the Greek letter, σ, which is the “Greek s.”