Transcript Document

The Standard Deviation as a
Ruler
Ch. 6
London Weather 9/15-9/17
•
•
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Who: Date and time
What: Temperature ( C)
Why: N/A
Where: original data gathered in Orpington,
SE London, data pulled from
http://weather.lgfl.org.uk
• When: 15/9/13 to 17/9/13
• How: data gathered by observation
Rescaling
• Celsius to Kelvin
𝐾 = ℃ + 273.15
• Celsius to Farenheit
9
℉ = ℃ + 32
5
Adding a constant to the data
• Shifts the whole distribution
• Mean increases/decreases by constant
• Standard deviation doesn’t change
Multiplying by a constant
• Scales the distribution
• Mean is multiplied by constant
• Standard deviation is multiplied by constant
Standardizing Data
• Data is converted to a universal scale so we
can compare apples to oranges
• Units are standard deviations
Standard Score (z-score)
𝑠𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐 − 𝑝𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟
𝑧=
𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛
𝑦−𝑦
𝑧=
𝑠
Which is better?
Barry Bonds, 73 HR 2001
Bonds
HR/600 PA: 66.0
Babe Ruth, 60 HR 1927
Ruth
HR/600 PA: 52.1
League
Average HR/600 PA: 9.2
SD HR/600 PA: 14.7
League
Average HR/600 PA: 3.4
SD HR/600 PA: 7.3
66.0 − 9.2
𝑧=
14.7
52.1 − 3.4
𝑧=
7.3