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