STAT3000
Section 1.3:
The Normal Distributions
Exploring Data on a Single Quantitative Variable
1. Always plot your data: make a graph, usually a
histogram or a stemplot.
2. Look for the overall pattern (shape, center,
spread) and for striking deviations such as
outliers.
3. Calculate a numerical summary to briefly
describe center and spread.
Sometimes the overall pattern of a large number of
observations is so regular that we can describe it by a
smooth curve = density curve
.
A density curve is a curve that
•
is always on or above the horizontal axis ( they
will not touch the horizontal axis ), and
•
has area exactly 1 underneath it.
A density curve describes the overall pattern of a
distribution.
The area under the curve and above any
33
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View Full Documentrange of values is the proportion of all observations
that fall in that range.
If X is approximately normal, then
•
X has a bellshaped density curve.
•
The density curve is perfectly
symmetric about its mean
μ
.
•
Its spread is determined by
σ
{notation X~ N(
μ
,
σ
)( variable x is
aprox normal and( mean and std
deviation for X)}.
•
The total area under any normal
curve is 1 (1 = 100%).
•
689599.7 Rule
•
There are an infinite number of
normal curves, one for each pair of
μ
and
σ
.
•
The standard normal is one very
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 Spring '08
 Staff
 Normal Distribution, Standard Deviation, standard normal distribution, density curve

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