STAT2003 Chapter Notes - Chapter 4-6: Ss 1, George E. P. Box, Passive Smoking
Ch 4. Understanding and Comparing Distributions, Ch 5. The Standard Deviation as a Ruler
and the Normal Model, Ch 6. Scatterplots, Association, and Correlation
Covers: 9/4, 9/6, 9/8, 9/11, 9/13, 9/15 (6 Lectures, Week 2 & 3)
Ch 4. Understanding and Comparing Distributions
Comparing Groups with Histograms
● Ex. Wind Speeds in the Hopkin Memorial Forest
○
■ Typical speed < 1mph
■ Small number of high wind days
■ One very windy day > 6 mph
■ IQR ~ 1.82 mph
○ May be interesting to compare winter (Oct - Mar) with summer (Apr -
Sep)....Comparing Seasons (Comparing Graphs)
○
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■ Summer is unimodal and skewed right whereas winter is less skewed and
nearly uniform
■ Typical summer wind < 1mph, a few days above 3mph
■ Winter wind often < 3mph and more spread out
■ Seems to be relatively calm in the summer but winter has windier days
(substantial)
■ Both the standard deviation and the IQR indicate that winter wind speeds
vary greater in comparison to summer speeds
● Comparisons Using Stem-and-Leaf charts
○ Ex.
■ This is called a ak-to-ak ste-and-leaf diagram
■ Here you can conclude that the Northeast and Midwest generally have
igger est egg idies this is hat the are oparig...tha the “outh
and West
■ Back-to-back charts are greatly adapted for comparisons of
numbers/figures
Comparing Groups with Boxplots
● Using Boxplots for Comparisons
○ Ex. 1 Windy Months...
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○ Note:
■ Are some months windier than others?
■ Compare April and July
■ That it is easy to spot outliers over the year with this view
○ Ex. 2. Wood vs. Steel Roller Coasters
○ Note:
■ Which type of roller coaster is faster? -Steel roller coasters are generally
faster.
■ Similar IQRs, but notice the difference in the ranges
■ One is a superfast steel roller coaster, but no exceptionally fast wooden
roller coasters exist
Outliers
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Document Summary
The standard deviation as a ruler and the normal model, ch 6. Covers: 9/4, 9/6, 9/8, 9/11, 9/13, 9/15 (6 lectures, week 2 & 3) May be interesting to compare winter (oct - mar) with summer (apr - Summer is unimodal and skewed right whereas winter is less skewed and nearly uniform. Typical summer wind < 1mph, a few days above 3mph. Winter wind often < 3mph and more spread out. Seems to be relatively calm in the summer but winter has windier days (substantial) Both the standard deviation and the iqr indicate that winter wind speeds vary greater in comparison to summer speeds. This is called a (cid:862)(cid:271)a(cid:272)k-to-(cid:271)a(cid:272)k(cid:863) ste(cid:373)-and-leaf diagram. Here you can conclude that the northeast and midwest generally have (cid:271)igger (cid:862)(cid:374)est egg i(cid:374)di(cid:272)es(cid:863) this is (cid:449)hat the(cid:455) are (cid:272)o(cid:373)pari(cid:374)gtha(cid:374) the outh and west. Back-to-back charts are greatly adapted for comparisons of numbers/figures. That it is easy to spot outliers over the year with this view.
