Presentation on theme: "More on Describing Distributions"— Presentation transcript:
1More on Describing Distributions AP StatisticsMore on Describing Distributions
2On the Docket… Homework Questions Notes: Numerical measures of center and spreadBoxplotsFinish Life Expectancy WorksheetIn Class ExampleStart the Homework
3Homework Questions and Collection On the Worksheet?1.8?1.14?1.16?
4Describing Distributions with Numbers Numerical CentersMean: x-barNot resistantMedian: MMidpoint of distributionArrange data from smallest to largest, if n is odd, the median is the middle number, if even, average the two center valuesIs resistant
5Measuring Spread Standard Deviation: Sx Shows how far the average value deviates from the meanFormulas:Variance Standard Deviation
6Properties of Standard Deviation The larger the standard deviation, the more spread out the observations are.S is not resistantMean and Standard Deviation are good for symmetric data.
7IQR: Interquartile Range Quartiles: Q1 and Q3:Q1 = median of values to the left of MQ3 = median of values to the right of MIQR = Q3 – Q15 Number Summary: Min, Q1, M, Q3, MaxBoxplot is based on 5 number summary
8IQR cont. Outliers: 1.5 x IQR above Q3 or below Q1 Median and IQR are Any value: less than Q1 – 1.5 x IQRgreater than Q x IQR
9Finish WorksheetSee p7 of Life Expectancy Worksheet
10The Trouble with Baseball (circa 2000) See handout for salariesEnter NY Yankees into list L1Enter LA Dodgers into list L2Enter Minnesota Twins into list L3
11Creating 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 clubsCompare the number of outliers for each team.Which of the LA Dodger Salaries might be outliers on the Yankees?
12More 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?