Unformatted text preview: Distributions & Graphs
Distributions & Graphs Variable Types
Variable Types Discrete (nominal) Sex, race, football numbers Continuous (interval, ratio) Temperature, Test score, Reaction time Frequency Distributions
Frequency Distributions Graphic representation of data Basic kinds of frequency distributions Easier to understand than raw numbers
Helps communicate to others
Ungrouped – simple tally
Grouped – used to simplify Uses Relative and cumulative frequency
Shape Common of Graphs
Common of Graphs
Bars show counts 6 Bar Chart (discrete) Frequency 4 2 0
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50 m Sex Frequency Histogram (continuous)
Scatterplot (2 variables)
Miles per Gallon 100 150 Horsepower 60.00 61.00 62.00 200 Height Inches 63.00 64.00 Distribution Shapes
Distribution Shapes Normal
Center
Spread
Shoulders
Skew
There will be numerical ways to describe all these, but for now, just consider the shape visually. Normal
Normal Central Tendency
Central Tendency Variability (spread)
Variability (spread) Central tendency and Variability Skew
Skew The tail! Kurtosis shoulders
Kurtosis shoulders Odd Shapes
Odd Shapes Modern Stat Graphs
Modern Stat Graphs Box plot
Stemleaf Boxplot
Boxplot Boxplot for a normal distribution
9 Largest C ase not an Outlier 8 7 Whisker or tail
75 %tile 6 5 Middle
50 Perc ent Median
25 %tile 4 3 2 Whisker or tail
Smallest C ase not an Outlier 1
N= 17 D1 Same distribution as a (sort of) histogram Boxplot with outliers
Boxplot with outliers
20 22 10 20 19 0
21 10
N= 21 Extreme Outlier
Outlier Outlier
Extreme Outlier Boxplot with Skewed Distribution
Boxplot with Skewed Distribution
30000 20000 224
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222 10000 0 10000
N= 227 volcano heights Exam and Course Distributions Psych Stats Fall 2007 Course Grades Sp 2008
Course Grades Sp 2008 Stemleaf diagram
Stemleaf 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) Normal distribution Stemleaf of volcano heights
Stemleaf 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 6.00 Extremes (>=18500) Stem width: 1000.00 Each leaf: 1 case(s) Final Grade Pct Sp 08
Final Grade Pct Sp 08 TotPct08 StemandLeaf Plot Frequency Stem & Leaf 12.00 Extremes (=<.48) 3.00 5 . 669 12.00 6 . 011333344444 18.00 6 . 555566677777889999 28.00 7 . 0000111122222223333333444444 34.00 7 . 5555555566666667777777888888889999 29.00 8 . 00000111111112222223333344444 13.00 8 . 5555566667788 16.00 9 . 0000011111123344
Note that SPSS has the boxplot 3.00 9 . 566
with larger numbers at the top, Stem width: .10 Each leaf: 1 case(s) but the stemleaf shows larger numbers at the BOTTOM, so one is backwards from the other. Definition
Definition Political party is an example of what kind of variable? 1 continuous 2 discrete
3 intensity
4 objective Definition
Definition A distribution with a long tail to the right (high) end is called ________
1 leptokurtic
2 negatively skewed
3 platykurtic
4 positively skewed Graphs
Graphs Which boxplot shows a skewed distribution?
2 1 4 3
8 12 10 6000 7
5000 10 8 6 4000 5 8 6 4 3000
6 4 3 2000 2
4 2 1000
2
N= 24 VAR00001 1
0 0
N= 406 Vehicle Weight (lbs. N= 0
19 VAR00002 N= 19 VAR00001 Discussion Question
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? ...
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 Spring '10
 Brannick
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