Presentation on theme: "More on Describing Distributions"— Presentation transcript:
1 More on Describing Distributions AP StatisticsMore on Describing Distributions
2 On the Docket… Homework Questions Notes: Numerical measures of center and spreadBoxplotsFinish Life Expectancy WorksheetIn Class ExampleStart the Homework
3 Homework Questions and Collection On the Worksheet?1.8?1.14?1.16?
4 Describing 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
5 Measuring Spread Standard Deviation: Sx Shows how far the average value deviates from the meanFormulas:Variance Standard Deviation
6 Properties 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.
7 IQR: 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
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 IQRgreater than Q x IQR
9 Finish WorksheetSee p7 of Life Expectancy Worksheet
10 The Trouble with Baseball (circa 2000) See handout for salariesEnter NY Yankees into list L1Enter LA Dodgers into list L2Enter 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 clubsCompare 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?