4-1 Chapter Four McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Describing Data: Displaying and Exploring Data

4-2Quartiles ie. 25% of observations fall into each part

4-3Quartiles Q2 Median 50% of data Median is same as the second quartile

4-4QuartilesQuartiles Quartiles (continued) Q2 Q1 Median 25% of data 50% of data

4-5QuartilesQuartiles Quartiles (continued) Q3 Q1 Q2 25% of data 50% of data 75% of data 100% of data Median

4-6 The Interquartile range is the distance between the third quartile Q 3 and the first quartile Q 1. This distance will include the middle 50 percent of the observations. Interquartile range = Q 3 - Q 1 This is a useful measure because it removes ‘outlier’ effect

4-7 Location of a Percentile L p = (n+1) n is the number of observations Notice, if P=50, then you get Median! Remember (n+1)/2 ? Useful for comparisons – eg. Performance in SAT of two students who took the test in different years

4-8 Exercise Do self-review 4-2, page 99 Do problem #3, page 100

4-9 Stock prices on 12 consecutive days for a major publicly traded company Example 2

4-10 Skewness - measure of symmetry in a distribution symmetric If the tail is longer towards more positive, it is a positive skew If the tail is longer towards zero (or more negative), it is a negative skew

4-11 Relative Positions of Mean, Median & Mode: Symmetric Distribution Mean=Median=Mode

4-12 Positively skewed Mean and median are to the right of the mode Rule: Median is always in the Middle Mode is always the peak Median divides the curve into 2 equal areas Mean weights the values

4-13 Negatively Skewed Mean and Median are to the left of the Mode Rule: Median is always in the Middle

4-14 Study this example in text (Pages 69-70)

4-15 Chapter Four Describing Data: Displaying and Exploring Data GOALS Accomplished in this Chapter TWO Compute and understand the coefficient of variation and the coefficient of skewness. ONE Develop and interpret quartiles and percentiles Goals