Distributions

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Distributions Graphs
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Variable Types

• Discrete (nominal)
• Sex, race, football numbers
• Continuous (interval, ratio)
• Temperature, Test score, Reaction time

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Frequency Distributions

• Graphic representation of data
• Easier to understand than raw numbers
• Helps communicate to others
• Basic kinds of frequency distributions
• Ungrouped simple tally
• Grouped used to simplify
• Uses
• Relative and cumulative frequency
• Shape

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Common of Graphs

• Bar Chart (discrete)
• Histogram (continuous)
• Scatterplot (2 variables)

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Distribution Shapes

• Normal
• Center
• Spread
• Shoulders
• Skew

There will be numerical ways to describe all
these, but for now, just consider the shape
visually.
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Normal
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Central Tendency
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Variability (spread)
Central tendency and Variability
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Skew
The tail!
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Kurtosis - shoulders
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Odd Shapes
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Modern Stat Graphs

• Box plot
• Stem-leaf

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Boxplot
Same distribution as a (sort of) histogram
Boxplot for a normal distribution
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Boxplot with outliers
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Boxplot with Skewed Distribution
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Exam and Course Distributions Psych Stats Fall
2007
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Course Grades Sp 2008
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Stem-leaf diagram

• Frequency Stem Leaf
• 1.00 2 . 0
• 2.00 3 . 00
• 3.00 4 . 000
• 4.00 5 . 0000
• 3.00 6 . 000
• 2.00 7 . 00
• 1.00 8 . 0
• Stem width 1.00
• Each leaf 1 case(s)

(Approximately) Normal distribution
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Stem-leaf of volcano heights

• Frequency Stem Leaf
• 8.00 0 . 25666789
• 8.00 1 . 01367799
• 23.00 2 . 00011222444556667788999
• 21.00 3 . 011224445555566677899
• 21.00 4 . 011123333344678899999
• 24.00 5 . 001122234455666666677799
• 18.00 6 . 001144556666777889
• 26.00 7 . 00000011112233455556678889
• 12.00 8 . 122223335679
• 14.00 9 . 00012334455679
• 13.00 10 . 0112233445689
• 10.00 11 . 0112334669
• 9.00 12 . 111234456
• 5.00 13 . 03478
• 2.00 14 . 00
• 3.00 15 . 667
• 2.00 16 . 25
• 2.00 17 . 29

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Final Grade Pct Sp 08

• TotPct08 Stem-and-Leaf Plot
• Frequency Stem Leaf
• 12.00 Extremes (lt.48)
• 3.00 5 . 669
• 12.00 6 . 011333344444
• 18.00 6 . 555566677777889999
• 28.00 7 . 0000111122222223333333444444
  
• 34.00 7 . 5555555566666667777777888888
  889999
• 29.00 8 . 0000011111111222222333334444
  4
• 13.00 8 . 5555566667788
• 16.00 9 . 0000011111123344
• 3.00 9 . 566
• Stem width .10
• Each leaf 1 case(s)

Note that SPSS has the boxplot with larger
numbers at the top, but the stem-leaf shows
larger numbers at the BOTTOM, so one is backwards
from the other.
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Definition

• Political party is an example of what kind of
  variable?
• 1 continuous
• 2 discrete
• 3 intensity
• 4 objective

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Definition

• A distribution with a long tail to the right
  (high) end is called ________
• 1 leptokurtic
• 2 negatively skewed
• 3 platykurtic
• 4 positively skewed

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Graphs

• Which boxplot shows a skewed distribution?

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2
3
1
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Discussion Question

• When might you prefer a graph to a table of
  numbers for presenting a result?
• Name a variable you think would be interesting
  for college students to see as a graph. What
  kind of data would you put in the graph? Why
  would it be of interest?