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5/16/11
Lecture 5
1
STOR 155 Introductory Statistics
Lecture 5: Density Curves and Normal
Distributions (I)
The
UNIVERSITY
of
NORTH CAROLINA
at
CHAPEL HILL
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Lecture 5
2
A problem about Standard Deviation
A variable has 5 possible values. The mean
is 125 and the standard deviation is 25. If
a sixth number of 125 is added in, what is
the new standard deviation?
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Lecture 5
3
To describe distribution of variable
X
• Plot your data:
– Stemplot, histogram, boxplot
• Look for overall pattern (shapes) + striking
deviations (outliers)
• Calculate appropriate numerical summaries
about center and spread
– Mean, median, mode
– Range, percentiles, quartiles, standard deviation
– Fivenumber summary, boxplot
– IQR and outliers
•
Make things easier with a
smooth curve
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Lecture 5
4
5/16/11
Lecture 5
5
Density Curve  A Math
Approximation
• To calculate probabilities, we define a
probability density function
f(x)
.
• The curve that plots
f(x)
is called the
corresponding density curve.
•
f(x)
satisfies:

f(x)
>= 0;
– The total area under the curve representing
f(x)
equals 1.
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Lecture 5
6
Density Curves
• Describe the overall shape of distributions
• Idealized
mathematical models for distributions
• Show patterns that are accurate enough for
practical purposes
• Always
on or above
the horizontal axis
• The total area under the curve is
exactly 1
• Areas under the curve represent relative
frequencies of observations
5/16/11
Lecture 5
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This note was uploaded on 11/18/2011 for the course STOR 155 taught by Professor Andrewb.nobel during the Summer '08 term at UNC.
 Summer '08
 AndrewB.Nobel

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