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Chapter 3: Variability
•Mean Sometimes Not Sufficient• Frequency Distributions•Normal Distribution• Standard Deviation
What City has Temperatures to My Liking?
•Person 1: Likes Seasons and Variability
•Person 2: Likes Consistency, Cool Temps
Average Temperature by City
(1961-1990)
Temperature
Proximity to Ocean
Latitude: South-North
Elevation
Climate:
• Precipitation
• Humidity
San Francisco
San Diego
30 60 90
30 60 90
30 60 90
30 60
30 60 90
Temperature Variation Across Cities in 2011
Boston
Austin
90Tampa Bay
Similar Mean, Different Distributions
SeattlePortland
Omaha
Boston
Normal Distribution
• Adolphe Quételet (1796-1874)• ‘Quetelet Index’: Weight / Height
(“Body Mass Index”)
Normal Distribution
Two Metrics:Mean and Standard Deviation
• A deviation is the difference between the mean and an actual data point.
• Deviations are calculated by taking each value and subtracting the mean:
deviation ix x deviation ix x
Calculating Standard Deviation
Mean
• Deviations cancel out because some are positive and others negative.
Summary the Deviation?
• Overall would be 0
• Not Useful
• Therefore, we square each deviation.
• We get the sum of squares (SS).
Sum of Squared Deviation
^2
• The sum of squares is a good measure of overall variability, but is dependent on the number of scores
• We calculate the average variability by dividing by the number of scores (n)
• This value is called the variance (s2)
Variance
• Variance is measured in units squared
• This isn’t a very meaningful metric so we take the square root value.
• This is the standard deviation (s)
Standard Deviation^2
53 70 87192 36
55Median
104