Section 1.2 Part II

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Section 1.2 Part II

• Special Problem Guidelines posted online start
  today!

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Standard Deviation A measure of spread

• Standard deviation looks at how far observations
  are from their mean.
• Its 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.

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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. MedianStandard Deviation vs. 5-Number
Summary

• 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.

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• 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)

• 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 persons 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
• (TI-83 STAT/Calc/1-var-Stats L1 after entering
  list into L1)

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You do! (Long Way Round)

• Let X
• What is the variance and standard deviation?

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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?

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Miami Heat Salaries1) 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