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σ
= .8, for example
σ
= 1.5
σ
= 3
µ
FIGURE 1.2
A family of normal curves with different values of
σ
.
Figure 1.2
illustrates different normal curves, all centered at the same value, and all
having the same area of “1,” but being different degrees of short and fat and tall and
thin. That is, each has a different value of σ, where a larger value means more vari-
ability among the resulting outcome values. Conversely, a small value means less
variability within your data set (e.g., more agreement/similarity among the respon-
dents' results). Compare the curve with a standard deviation of 0.8 to the curve with
a standard deviation of 3. The former is taller and thinner—thus having less vari-
ability—than the latter.
So, to summarize, a normal curve is determined by its “μ” and its “σ,” and
smallerσ↔taller,thinnercurve
largerσ↔shorter,fattercurve
SIDEBAR: THE NORMAL CURVE FORMULA
OK, so returning to the normal curve, we feel obliged as UX research professionals to tell you that
there is a mathematical formula for a normal curve, but, happily, we generally don't need to know
it! But…maybe you're curious. We'll show it to you, but irst you need to promise not to let it intimi-
date you into not reading the rest of the topic!! Promise? OK, here we go… The normal distribution
mathematical function,
f
N
(
x
), given values of μ and σ, is depicted in
Figure 1.3
.
2
x - µ
σ
1
2
µ
σ
1
-
x
=
e
ƒ
N
√
2
π ⋅
σ
FIGURE 1.3
The mathematical expression for the normal curve.
It isn't pretty! Even the exponent has an exponent; but, it is what it is. Luckily, you don't have to
think about this formula for the rest of the topic.
1.2.1
FINDING PROBABILITIES OF COMPLETION TIMES
OR SATISFACTION LEVELS, OR ANYTHING ELSE,
ON A NORMAL CURVE
We mentioned earlier that inding an area under a normal curve between any two
points is the same as inding the probability that you get a result (satisfaction value,
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