More on Describing Distributions AP Statistics More on Describing Distributions

On the Docket… Homework Questions Notes: Numerical measures of center and spread Boxplots Finish Life Expectancy Worksheet In Class Example Start the Homework

Homework Questions and Collection On the Worksheet? 1.8? 1.14? 1.16?

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

Measuring Spread Standard Deviation: Sx Shows how far the average value deviates from the mean Formulas: Variance Standard Deviation

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.

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

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

Finish Worksheet See p7 of Life Expectancy Worksheet

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

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?

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?

Homework 1.31, 1.35, 1.36, 1.41, 1.43