Transcript Document

Lectures 3-4
Week2
• Describing Data with Numerical
Values
• (Chapter 2)
7/17/2015
Chapter 2
1
Terminology and Types of Measures
• Measures associated to Population:
Parameters
• Measures associated to a sample: Statistics
Population
7/17/2015
Chapter 2
Sample
2
Two kinds of measures
• Measures of Location, center, position
• Measures of dispersion, shape, variability
7/17/2015
Chapter 2
3
Measures of location
• The mean
– Example
• The median
– Example
• The mode
– Example
7/17/2015
Chapter 2
4
Relationship between mean and
median
•
•
•
•
Median is robust
If data symmetric, mean=median
If right-skewed data, mean shifts to right
If left-skewed data, mean shifts to left.
Median unchanged.
7/17/2015
Chapter 2
5
Measures of Dispersion
• Range
– Example
• Variance
– Shortcut formula
– Example
• Standard deviation
– Example
Advantage: has same unit as data.
7/17/2015
Chapter 2
6
Practical significance of standard
deviation
• Chebychev’s Theorem
– Example
• Empirical rule (symmetric data)
– Example
• Measures of relative standing
– Z-score, Outliers
– Example
7/17/2015
Chapter 2
7
Quartiles, Box-plots
•
•
•
•
•
•
•
Q1=1st quartile
Q2=median
Q3=3rd quartile
IQR=Q3-Q1
Computing Formulae and Examples
Box-plot
Outliers
7/17/2015
Chapter 2
8