Shape of distribution (0)

SHAPE  OF 
DISTRIBUTION
Shapes
What  terms  are used to describe 
shapes of
• people?
• buildings?
• countries?
Examples  of distribution
3
Shape of distribution
Use the term  “skew”
• no skew
• right skew
•  left  skew
No skew
x
x

Right skew (or  positive  
skew)
x
x

Left skew (or  negative  
skew)
x
~  x
Remember
Mean  moves in the direction of 
the skewness
Example
Number of burglaries  reported  
in 1996 for  nine  
universities .
61, 11, 1, 3, 2, 30, 18, 3, 7
(a)  Find the mean and median
(b)Determine the type of 
skewness of the distribution
Skewness of distributions
What is the skewness of the 
following  distributions?
Income
Easy test
Hard test
10
Coefficient of Skewness
11
Interpreting Coefficient of Skewness
Values  range from -3 to +3
Box plot
Also known as box-and- whisker plot.
13
Example
Draw  a box-plot for the following 
data:
15, 13, 6, 5, 12, 28, 22, 18
Skewness from box plot
15
Outliers
•An extremely high or an extremely 
low data value when compared with 
the rest of the data values.
• Discuss examples
When is a value an 
outlier?
When the value is
a) greater  than  Q3 + 1.5(interquartile range)
b) less than Q1 – 1.5(interquartile range) 
Example
Check  this data for outliers
5   6   12   13   15   18    
22   50 

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