4-1

Chapter

Four

McGraw-Hill/Irwin

© 2006 The McGraw-Hill Companies, Inc., All Rights Reserved.

Describing Data: Displaying and Exploring Data

4-2

D iv id e a se t o f

o b serv a tio n s

in to fo u r

eq u a l p a rts .

QuartilesQuartiles

ie. 25% of observations fall into each

part

4-3

QuartilesQuartilesL o ca te th e m ed ia n ,

(5 0 th p ercen tile )

Q2Median

50% of data

Median is same as the second quartile

4-4

QuartilesQuartilesQuartilesQuartilesL o ca te th e m ed ia n ,

(5 0 th p ercen tile )

th e first q u artile

(2 5 th p ercen tile )

Quartiles (continued)

Q2Q1 Median

25% of data

50% of data

4-5

QuartilesQuartilesQuartilesQuartilesL o ca te th e m ed ia n ,

(5 0 th p ercen tile )

first q u a rtile (2 5 th p ercen tile )

a n d th e 3rd q u artile

(7 5 th p ercen tile )

Quartiles (continued)

Q3

Q1Q2

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 Q3 and the first quartile Q1.

This distance will include the middle 50

percent of the observations.

Interquartile range = Q3 - Q1

This is a useful measure because it removes ‘outlier’ effect

4-7

Location of a PercentileLocation of a Percentile

P

1 0 0

w h ere

P is th e d e s ired p e rcen tile

Lp = (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

4-10

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

M o d e

M ed ia n

M ea n

4-12

Positively skewed

Mean and median are to the right of the mode.

M o d e

M ed ia n

M ea n

3- 12

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.

M o d eM ea n

M ed ia n

3- 13

Rule: Median is always in the Middle

4-14

Study this example in text (Pages

69-70)

4-15

Chapter FourDescribing Data: Displaying and Describing Data: Displaying and

Exploring DataExploring Data

GOALS Accomplished in this Chapter

TWOCompute and understand the coefficient of variation and the coefficient of skewness.

ONE Develop and interpret quartiles and percentiles

Goals