101 Ch. 6 - Chapter 6 The Standard Deviation as a Ruler and...

Info iconThis preview shows pages 1–18. Sign up to view the full content.

View Full Document Right Arrow Icon
Chapter 6 The Standard Deviation as a Ruler and the Normal Model
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Normal Distributions Bell Curve Physical Characteristics Examples Heights Weights Lengths of Bird Wings Most important distribution in statistics
Background image of page 2
Normal Distributions Curve is always above the x-axis The tails never reach the x-axis They continue on to infinity and –infinity Area under entire curve = 1 or 100% Mean = Median This means the curve is symmetric
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Normal Distributions Two parameters (not calculated, i.e. do not come from the data) Mean μ (pronounced “meeoo”) Locates center of curve Splits curve in half Shifts curve along x-axis
Background image of page 4
Normal Distributions Standard deviation σ (pronounced “sigma”) Controls spread of curve Smaller σ makes graph tall and skinny Larger σ makes graph flat and wide Ruler of distribution Write as N( μ,σ)
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Perfect World Wouldn’t everyone like it if there was a perfect world? In Statistics there is!!!! We call it the Standard Normal Distribution.
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Standard Normal (Z) World Perfectly symmetric Centered at zero Half numbers below the mean and half above. Total area under the curve is 1. Can fill in as percentages across the curve.
Background image of page 8
Standard Normal Distribution Puts all normal distributions on same scale z has center (mean) at 0 z has spread (standard deviation) of 1 σ μ - = y z
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Standard Normal Distribution z = # of standard deviations away from mean μ Negative z, number is below the mean Positive z, number is above the mean Written as N(0,1)
Background image of page 10
Portal from X-world to Z-world z has no units (just a number) Puts variables on same scale Center (mean) at 0 Spread (standard deviation) of 1 Does not change shape of distribution s y y z - =
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Standardizing Variables z = # of standard deviations away from mean Negative z – number is below mean Positive z – number is above mean
Background image of page 12
Standardizing Y ~ N(70,3). Standardize y = 68. y = 68 is 0.67 standard deviations below the mean 67 . 0 3 70 68 - = - = - = σ μ y z
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Standardizing Notice the difference between Y and y Y denotes an entire distribution; all possible values of the distribution, the shape, the center, the spread y denotes a single value ONLY Can be generalized to all capital letters Z and z X and x
Background image of page 14
Standardizing N(70,3) N(0,1)
Background image of page 15

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Standardizing Y ~ N(70,3). Standardize y = 74 y = 74 is 1.33 standard deviations above mean 33 . 1 3 70 74 = - = - = σ μ y z
Background image of page 16
Standardizing N(70,3) N(0,1)
Background image of page 17

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 18
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/30/2008 for the course STAT 101 taught by Professor Graham during the Spring '08 term at Iowa State.

Page1 / 56

101 Ch. 6 - Chapter 6 The Standard Deviation as a Ruler and...

This preview shows document pages 1 - 18. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online