Chapter 3
The Normal Distributions
1

How to explore a distribution
•
Graphical summary (a plot, a graph, a histogram)
•
Overall pattern (shape, center, spread); outliers
•
Numerical summary to describe center and
spread.
•
Another way:
Density Curve

Histogram of the test scores of 947
students
The smooth curve
drawn over the
histogram is called a
density curve
.
This curve is a
mathematical
model
for the distribution.

Histograms and areas
The total area under a the
histogram is equal to 1 (or
100%).
The shaded area
represents the proportion
of scores that are less
than or equal to
6.0.
(This proportion is equal
to 0.303 or 30.3%).

Density curves and areas
If the scale is adjusted so
the total area under the
curve is exactly 1, then
this curve is called a
density curve
.
The proportion of the
area to the left of 6.0 is
now equal to 0.293.
A density curve can be a
good approximation
to
the distribution.

Density Curve: Definition
A
density curve
is a curve that:
•
Always on or above the horizontal axis
•
has an area of exactly 1 underneath it
Area under the curve and above any range of
values is the proportion of all observations that
fall in that range.

Density Curves
Our measures of center and spread apply to density curves as
well as to actual sets of observations
.
•
The
median
of a density curve is the
equal-areas point
, the