9/7/2009

Questions on descriptive statistics from Chapter 4

• Standard deviation contest: You must choose 4 numbers from the set {0, 1, 2, ..., 10} with repeats allowed.
  • Choose 4 numbers that have the smallest possible standard deviation.
  • Choose 4 numbers that have the largest possible standard deviation.

Empirical Rule

• If the histogram of values in a data set can be reasonalby approximated by a Normal curve, then
  • approximately 68% of the observations are within 1 standard deviation of the mean
  • approximately 95% of the observations are within 2 standard deviation of the mean
  • approximately 99.7% of the observations are within 3 standard deviation of the mean

Linear Transformations

• Let x₁, …, x_n be a data collection and consider the linear transformation x_new=a+bx_i, i=1, …, n.

Example

Consider the following monthly average temperatures for the city of New York.

Month	Jan.	Feb.	March	April	May	June	July	Aug.	Sept.	Oct.	Nov.	Dec.
Temp (oF)	32	33	41	52	62	72	77	75	68	58	47	35

Find the measures of center and spread for degrees centigrade.  Let x_new = 5/9*(x-32).

Summarizing Bivariate Data

• Scatterplots
• Applets

Common Types of Relationships

• No Association
• Positive Association
• Negative Association

Scatterplot Smoothing

• 1970 Draft Lottery Data

Measuring the strength of assocation

• Pearson’s correlation coefficient

Properties of r

• r > 0 indicates positive association.
• r < 0 indicates negative association.
• Extreme values r = 1 and r = -1 indicate perfect linear association.
• The value of r remains unchanged if the unit of measurement of X, Y, or both changes.
• r measures only the strength of linear association between two variables.

Class Activity

• Guessing Correlations
• Another Applet for Guessing Correlations

Please read Sections 5.1, 5.2, and 5.3 for class on Monday