1. More on Describing Distributions
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 Q 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. That’s a sixfold increase. Why is this a problem for baseball?

13. Homework
1.31, 1.35, 1.36, 1.41, 1.43