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 ( )

Temperature Proximity to Ocean Latitude: South-North Elevation Climate: Precipitation Humidity

San Francisco San Diego Temperature Variation Across Cities in 2011 Boston Austin 90 Tampa Bay

Similar Mean, Different Distributions Seattle Portland Omaha Boston

Normal Distribution Adolphe Quételet ( ) ‘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: 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 (s 2 ) 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

Median 104