AP Statistics

1
AP Statistics

• More on Describing Distributions

2
On the Docket

• Homework Questions
• Notes
• Numerical measures of center and spread
• Boxplots
• Finish Life Expectancy Worksheet
• In Class Example
• Start the Homework

3
Homework Questions and Collection

• On the Worksheet?
• 1.8?
• 1.14?
• 1.16?

4
Describing Distributions with Numbers

• Numerical Centers
• Mean x-bar
• Not resistant
• Median M
• Midpoint of distribution
• Arrange data from smallest to largest, if n is
  odd, the median is the middle number, if even,
  average the two center values
• Is resistant

5
Measuring Spread

• Standard Deviation Sx
• Shows how far the average value deviates from
  the mean
• Formulas
• Variance Standard Deviation

6
Properties of Standard Deviation

• The larger the standard deviation, the more
  spread out the observations are.
• S is not resistant
• Mean and Standard Deviation are good for
  symmetric data.

7
IQR Interquartile Range

• Quartiles Q1 and Q3
• Q1 median of values to the left of M
• Q3 median of values to the right of M
• IQR Q3 Q1
• 5 Number Summary Min, Q1, M, Q3, Max
• Boxplot is based on 5 number summary

8
IQR cont.

• Outliers 1.5 x IQR above Q3 or below Q1
• Median and IQR are
• Any value less than Q1 1.5 x IQR
• greater than Q3 1.5 x IQR

9
Finish Worksheet

• See p7 of Life Expectancy Worksheet

10
The Trouble with Baseball (circa 2000)

• See handout for salaries
• Enter NY Yankees into list L1
• Enter LA Dodgers into list L2
• Enter Minnesota Twins into list L3

11
Creating Parallel Boxplots

• Follow me for instructions
• Questions
• Since LA has the highest median salary, does it
  therefore have the highest total payroll?
• Compare the variation of the three ball clubs
• Compare the number of outliers for each team.
• Which of the LA Dodger Salaries might be outliers
  on the Yankees?

12
More Questions

• What kind of skew do the distributions exhibit?
• What quartile would the Twins outliers be in if
  they were on the Dodgers?
• For Minnesota, the Min and Q1 are the same, why
  is this the case?
• The total payroll for the yankees is 93.3
  million. For the Twins, it is 15.4 million.
  Thats a sixfold increase. Why is this a problem
  for baseball?

13
Homework

• 1.31, 1.35, 1.36, 1.41, 1.43