Describing Data Displaying and Exploring Data Chapter Four

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

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

3 Quartiles Median Q 2 50% of data Median is same as the second quartile

4 Quartiles Q 1 Median Q 2 25% of data 50% of data Quartiles (continued)

5 Quartiles Q 1 Median Q 2 Q 3 25% of data 50% of data 75% of data 100% of data Quartiles (continued)

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

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

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

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

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

Positively skewed Mean and median are to the right of the mode. Rule: Median is always in the Middle 3 - 12 12 Mode is always the peak Median divides the curve into 2 equal areas Mean weights the values

3 - 13 13 Negatively Skewed Mean and Median are to the left of the Mode. Rule: Median is always in the Middle

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

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