Yesterdays Homework Assignment

1
Yesterdays Homework Assignment

• Complete Problems 1.19-1.22, 1.24-1.30 Be
  prepared to discuss tomorrow.
• Short quiz on section 1.1 tomorrow!

2
Housekeeping

• Please enter the following data into your
  calculators. Name the first set Bonds and the
  second set Aaron. If you have questions let me
  know!

Bonds
Aaron
3
Wednesdays Highlights

• Percentile of a distribution tells
• Ogives show
• Time plots display information
• Trends and seasonal variation

4
Describing Distributions with Numbers (1.2)

• Who is baseball greatest homerun hitter?
• Summer of 1998 McGwire and Sosa pursued baseballs
  single season homerun record (Roger Maris)
• McGwire eventual set a new record of 70
• In 2001, Bonds set a new record of 73.

5
Describing Distributions with Numbers (1.2)

• How does Bonds mark of 73 fit with his career?

• How should we display this information?
• SOCS
• Spread __________
• Outliers __________
• Center __________
• Shape __________

6
Decisions Through Data Measures of
CenterVideo 4 (1142)D\VIDEO_TS\VTS_04_1.VOB
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Measuring Center Median

• The midpoint of a distribution the number such
  that half the observations are smaller and the
  other half are larger.
• Arrange all observations in order of size,
  generally smallest to largest
• If number of observations n is odd, the median M
  is the center observation of the list.
• If the number of observations n is even, the
  median M is the mean of the two center
  observations in the ordered list.

8
Measuring Center Mean

• Most common measure of center of a distribution
• Found by adding all values of an observation and
  then dividing by number of observations.

9
Lets compare the mean and median of Bonds with
Hank Aaron
Bonds homerun totals
Hank Aarons homerun totals
Find the mean and median for each baseball player
10
Measuring Spread the quartiles

• Mean and median are good measures of centers, but
  dont always tell the whole story.
• Range measures difference between largest and
  smallest observations. Outliers can impact this
  value.
• Quartiles mark out the middle half
• 1st quartile lies one-quarter of the way up the
  list
• 3rd quartile lies three-quarters of the way up
  the list.

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The Quartiles Q1 Q3

• Arrange the observations in increasing order and
  locate the median M.
• The first quartile Q1 is the lower median of the
  overall median of observations.
• The third quartile Q3 is the upper median of the
  overall median of observations.

12
The IQR (Interquartile Range)

• The distance between the first and third
  quartiles is a simple spread covering the middle
  half of the data.
• IQR Q3 Q1
• The IQR acts as a basic rule of thumb for
  identifying suspected outliers.

13
Outliers The 1.5 X IQR Criterion

• We call an observation an outlier if it falls
  more than 1.5 times the IQR above the third
  quartile or below the first quartile.
• Lets look at Bonds home totals
• IQR Q3-Q1 41 25 16
• Q3 (1.5 X IQR) 41 (1.5 X 16) 65 (upper
  cuttoff)
• Q1 (1.5 X IQR) 25 (1.5 X 16) 1 (lower
  cuttoff)
• What about Bonds 73 homeruns in 2001?

14
Five Number Summary

• Consist of the smallest observation, the first
  quartile (Q1), the median (M), the third quartile
  (Q3), and the largest observation.
• Minimum Q1 M Q3 Maximum
• The five number summary for
• Bonds-
• Hank Aaron-

15
Using the five number summary to make a graph
(Boxplot)

• Show less detail than histograms or stemplots
• Best used for side-by-side comparison of more
  than one distribution
• Can be horizontal or vertical

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Decisions Through Data BoxplotsVideo 5
(957)D\VIDEO_TS\VTS_05_1.VOB
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Boxplots

• First locate the median
• Then look at spread
• Quartiles show middle half of the data
• Extremes show spread of entire data set
• How do Bonds and Aaron compare?

18
Boxplots and Symmetry

• If the distribution is symmetric, the first and
  third quartiles are equally distant from the
  median.
• In distributions that are skewed to the right,
  the third quartile is farther above the median
  than the first quartile is below the median.
• How would you describe Bonds and Aarons boxplots?

19
(No Transcript)
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Outliers and Modified Boxplots

• Outliers concealed in a regular boxplot
• Modified boxplots plot outliers as isolated points

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Boxplot (Modified)

• A graph of the five-number summary, with outliers
  plotted individually
• A central box spans the quartiles
• A line in the box marks the median
• Observations more than 1.5 X IQR outside the
  central box are plotted individually
• Lines extend from the box to the smallest and
  largest observations that are not outliers.

22
Tonights HW

• Exercises 1.32, 1.34, 1.35 on pg 41.
• Exercises 1.36, 1.38, 1.39 on pgs 47/48.
• Please read pgs 48-62 for Monday!
• Also, dont forget about Special Project 0!