Basic Practice of Statistics - 3rd Edition by klutzfu43

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									Basic Practice of Statistics - 3rd Edition

  Question: What is the average height of students in this class?

Chapter 1
Picturing Distributions with Graphs

  Answer: Easy, ask everyone the height, and then find the

average (mean).
  Question: What is the average height of students in

University of Utah?
  Answer: Seems complicated. Too many people, it will be

difficult to ask everyone. Ask a sufficiently large number of people (but still small compared to the total size of students) and make an estimate using tools from STATISTICS.

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Statistics
  1. How do we select the people to ask? How many people

should we ask?
  2. How do we make an estimate ?   3. Our estimate will be probably be a little different from the

true value. Can we say how close it is to the true value?

Statistics is a science that involves the extraction of information from numerical data obtained during an experiment or from a sample. It involves the design of the experiment or sampling procedure, the collection and analysis of the data, and making inferences (statements) about the population based upon information in a sample.

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Individuals and Variables
name megan ryan jacob antony ali guillermo hao nicos susan major bs egr ba bs egr bs bs ba ba score 25 35 40 50 22 24 31 35 24 gpa 3 2.5 3.5 2.5 2.6 2.3 3.4 3.3 2.9

  Individuals
  the objects described by a set of data   may be people, animals, or things

  Variable
  any characteristic of an individual   can take different values for different individuals

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Variables
  Places an individual into one of several groups or categories

Case Study
The Effect of Hypnosis on the Immune System
reported in Science News, Sept. 4, 1993, p. 153

  Takes numerical values for which arithmetic operations such as

adding and averaging make sense

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Case Study
The Effect of Hypnosis on the Immune System Objective: To determine if hypnosis strengthens the disease-fighting capacity of immune cells.

Case Study
  65 college students.
  33 easily hypnotized   32 not easily hypnotized

  white blood cell counts measured   all students viewed a brief video about the immune system.

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Case Study
  Students randomly assigned to one of three conditions
  subjects hypnotized, given mental exercise   subjects relaxed in sensory deprivation tank   control group (no treatment)

Case Study
  white blood cell counts re-measured after one week   the two white blood cell counts are compared for each

group
  results   hypnotized group showed larger jump in white blood cells   “easily hypnotized” group showed largest immune enhancement

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Case Study
Variables measured

Case Study
Weight Gain Spells Heart Risk for Women

quantitative

  Pre-study white blood cell count   Post-study white blood cell count

“Weight, weight change, and coronary heart disease in women.” W.C. Willett, et. al., vol. 273(6), Journal of the American Medical Association, Feb. 8, 1995. (Reported in Science News, Feb. 4, 1995, p. 108)

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Case Study
Weight Gain Spells Heart Risk for Women Objective: To recommend a range of body mass index (a function of weight and height) in terms of coronary heart disease (CHD) risk in women.
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Case Study
  Study started in 1976 with 115,818 women aged 30 to 55

years and without a history of previous CHD.
  Each woman’s weight (body mass) was determined.   Each woman was asked her weight at age 18.

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Case Study
  The cohort of women were followed for 14 years.   The number of CHD (fatal and nonfatal) cases were counted

Case Study
Variables measured

(1292 cases).

categorical

  Incidence of coronary heart disease   Smoker or nonsmoker   Family history of heart disease

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Distribution
  Tells what values a variable takes and how often it takes these

Displaying Distributions
  Categorical variables
  Pie charts   Bar graphs

values
  Can be a table, graph, or function

  Quantitative variables
  Histograms   Stemplots (stem-and-leaf plots)

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Class Make-up on First Day
Data Table
Year Freshman Sophomore Junior Senior Total
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Class Make-up on First Day
Pie Chart

Count 18 10 6 9 43

Percent 41.9% 23.3% 14.0% 20.9% 100.1%
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Class Make-up on First Day
Bar Graph

Example: U.S. Solid Waste (2000)
Data Table
25.9 12.8 18.0 86.7 24.7 15.8 12.7 27.7 7.5 231.9
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Material Food scraps Glass Metals Paper, paperboard Plastics Rubber, leather, textiles Wood Yard trimmings Other Total
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Weight (million tons)

Percent of total 11.2 % 5.5 % 7.8 % 37.4 % 10.7 % 6.8 % 5.5 % 11.9 % 3.2 % 100.0 %
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Example: U.S. Solid Waste (2000)
Pie Chart

Example: U.S. Solid Waste (2000)
Bar Graph

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Histograms
  For quantitative variables that take many values   Divide the possible values into

Histograms: Class Intervals
(we will only
  How many intervals?
  One rule is to calculate the square root of the sample size, and

consider equal widths)
  Count how many observations fall in each interval (may

round up.
  Size of intervals?
  Divide range of data (max-min) by number of intervals desired,

change to percents)
  Draw picture representing distribution

and round to convenient number
  Pick intervals so each observation can only fall in exactly

one interval (no overlap)
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Case Study
Weight Data
Introductory Statistics class Spring, 1997 Virginia Commonwealth University

Weight Data

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Weight Data: Frequency Table
Weight Group 100 - <120 120 - <140 140 - <160 160 - <180 180 - <200 200 - <220 220 - <240 240 -<260 260 -<280 sqrt(53) = 7.2, ; range (260-100=160) / 8 = Count 12 7 8 12 4 1 0 1 7

Weight Data: Histogram
Number of students
100 120 140

160 180 200 Weight

220 240

260

280

* Left endpoint is included in the group, right endpoint is not.

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Examining the Distribution of Quantitative Data
  Overall pattern of graph   Deviations from overall pattern   Shape of the data   Center of the data   Spread of the data (Variation)   Outliers

Shape of the Data
  Symmetric
  bell shaped   other symmetric shapes

  Asymmetric
  right skewed   left skewed

  Unimodal, bimodal

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Symmetric Bell-Shaped

Symmetric Mound-Shaped

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Symmetric Uniform

Asymmetric Skewed to the Left

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Asymmetric Skewed to the Right

Outliers
  Extreme values that fall outside the overall pattern
  May occur naturally   May occur due to error in recording   May occur due to error in measuring   Observational unit may be fundamentally different

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Stemplots
(Stem-and-Leaf Plots)   For quantitative variables   Separate each observation into a (first part of the number) and a (the remaining part of the number)   Write the stems in a vertical column; draw a vertical line to the right of the stems   Write each leaf in the row to the right of its stem; order leaves if desired

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Weight Data

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Weight Data: Stemplot
(Stem & Leaf Plot)

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10 11 12 13 5 14 15 2 16 17 18 19 2 20 21 22 23 24 25 26

192 152 135

Weight Data: Stemplot
(Stem & Leaf Plot)

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10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

0166 009 0034578 00359 08 00257 555 000255 000055567 245 3 025 0

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Extended Stem-and-Leaf Plots
If there are very few stems (when the data cover only a very small range of values), then we may want to create more stems by splitting the original stems.

Extended Stem-and-Leaf Plots
: if all of the data values were between 150 and 179, then we may choose to use the following stems:

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Leaves 0-4 would go on each upper stem (first “15”), and leaves 5-9 would go on each lower stem (second “15”).

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Time Plots
  A time plot shows behavior over time.   Time is always on the horizontal axis, and the variable being

Class Make-up on First Day
(Fall Semesters: 1985-1993)

measured is on the vertical axis.
  Look for an overall pattern (trend), and deviations from this

trend. Connecting the data points by lines may emphasize this trend.
  Look for patterns that repeat at known regular intervals

(seasonal variations).

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Basic Practice of Statistics - 3rd Edition

Average Tuition (Public vs. Private)

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