Download cms/lib04/CA01000848/Centricity/Domain/2671/Section 5.1 Day 1

(Day 1)
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So far, we have used histograms to represent
the overall shape of a distribution. Now
smooth curves can be used:
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If the curve is symmetric, single peaked, and
bell-shaped, it is called a normal curve.
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Plot the data: usually a histogram or a stem
plot.
Look for overall pattern
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Shape
Center
Spread
Outliers
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Choose either 5 number summary or “Mean
and Standard Deviation” to describe center
and spread of numbers
◦ 5 number summary used when there are outliers
and graph is skewed; center is the median.
◦ Mean and Standard Deviation used when there are
no outliers and graph is symmetric; center is the
mean
Now, if the overall pattern of a large number of
observations is so regular, it can be described by a
normal curve.
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The tails of normal curves fall off quickly.
There are no outlier
s
There are no outliers.
The mean and median are the same number,
located at the center (peak) of graph.
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Most histograms show the “counts” of
observations in each class by the heights of
their bars and therefore by the area of the
bars.
◦ (12 = Type A)
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Curves show the “proportion” of observations
in each region by the area under the curve.
The scale of the area under the curve equals
1. This is called a density curve.
◦ (0.45 = Type A)
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Median: “Equal-areas” point – half area is to the
right, half area is to the left.
Mean: The balance point at which the curve
would balance if made of a solid material (see
next slide).
Area: ¼ of area under curve is to the left of
Quartile 1, ¾ of area under curve is to the left of
Quartile 3. (Density curves use areas “to the
left”).
Symmetric: Confirms that mean and median are
equal.
Skewed: See next slide.
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The mean of a skewed distribution is pulled
along the long tail (away from the median).
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Uniform Distributions (height = 1)
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If the curve is a normal curve, the standard
deviation can be seen by sight. It is the point
at which the slope changes on the curve.
A small standard
deviation shows
a graph which is
less spread out,
more sharply
peaked…
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Carl Gauss used standard deviations to
describe small errors by astronomers and
surveyors in repeated careful measurements.
A normal curve showing the standard
deviations was once referred to as an “error
curve”.
The 68-95-99.7 Rule shows the area under
the curve which shows 1, 2, and 3 standard
deviations to the right and the left of the
center of the curve…more accurate than by
sight.
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More about 68-95-99.7 Rule, z-scores, and
percentiles…
We will be doing group activities. Please
bring your calculators and books!!!
Homework: None… 