Download 1.2 PII

Section 1.2 Part II
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Special Problem Guidelines posted
online – start today!
Standard Deviation: A measure of
spread
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Standard deviation looks at how far
observations are from their mean.
 It’s the natural measure of spread for the
Normal distribution
 We like s instead of s-squared (variance)
since the units of measurement are easier to
work with (original scale)
 S is the average of the squares of the
deviations of the observations from their
mean.
Etc…
S, like the mean, is strongly influenced
by extreme observations. A few outliers
can make s very large.
 Skewed distributions with a few
observations in the single long tail =
large s. (S is therefore not very helpful in this case)
 As the observations become more
spread about the mean, s gets larger.
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Mean vs. Median
Standard Deviation vs. 5-Number Summary
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The mean and standard deviation are more common
than the median and the five number summary as a
measure of center and spread.
 No single # describes the spread well.
 Remember: A graph gives the best overall picture of
a distribution. ALWAYS PLOT YOUR DATA!
 The choice of mean/median depends upon the shape
of the distribution.
When dealing with a skewed distribution, use the
median and the 5# summary.
When dealing with reasonably symmetric
distributions, use the mean and standard deviation.
The variance and standard deviation are…
LARGE if observations are widely spread about
the mean
SMALL if observations are close to the mean
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Degrees of Freedom (n-1)
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Definition: the number of independent pieces
of information that are included in your
measurement.
Calculated from the size of the sample. They
are a measure of the amount of information
from the sample data that has been used up.
Every time a statistic is calculated from a
sample, one degree of freedom is used up.
If the mean of 4 numbers is 250, we have
degrees of freedom  (4-1) = 3. Why?
____ ____ ____ ____ mean = 250
If we freely choose numbers for the first 3
blanks, the 4th number HAS to be a certain
number in order to obtain the mean of 250.
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A person’s metabolic rate is the rate at which
the body consumes energy. Metabolic rate is
important in studies of weight gain, dieting,
and exercise. Here are the metabolic rates of
7 men who took part in a study of dieting:
1792 1666 1362 1614 1460 1867 1439
Find the mean
Column 1: Observations (x)
Column 2: Deviations
Column 3: Squared deviations
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(TI-83: STAT/Calc/1-var-Stats L1 after entering list into L1)
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You do! (Long Way Round)
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Let X = 3,7,15, 23
What is the variance and standard
deviation?
You do! (using 1 Var Stats)
During the years 1929-1939 of the Great
Depression, the weekly average hours
worked in manufacturing jobs were 45,
43, 41, 39, 39, 35, 37, 40, 39, 36, and
37. What is the variance and standard
deviation?
Miami Heat Salaries
1) Suppose that each member receives
a $100,000 bonus. How will this
effect the
center, shape, and spread?
2) Suppose that each player
is offered 10%
increase in base salary.
What happened to
the centers and spread?
Player
Salary
Shaq
27.7
Eddie Jones
13.46
Wade
2.83
Jones
2.5
Doleac
2.4
Butler
1.2
Wright
1.15
Woods
1.13
Laettner
1.10
Smith
1.10
Anderson
.87
Dooling
.75
Wang
.75
Haslem
.62
Mourning
.33