1. Exploring Data
Chapter 1

2. Patterns from Histogram A
Center: the value that divides the observations roughly in half
Spread (variability): the extent of the data from smallest to largest value

3. Histogram A example center: 35, spread: 25 to 45

4. Histogram A example
center, spread

5. Patterns from Histogram B
Center: the value that divides the observations roughly in half
Spread (variability): the extent of the data from smallest to largest value
Shape: overall appearance of distribution

6. Histogram B example
skewed right

7. Histogram B example
skewed left

8. Histogram B example symmetrical, mound shaped

9. Histogram B example
uniform

10. Histogram B example
bimodal

11. Patterns from Histogram C
Center: the value that divides the observations roughly in half
Spread (variability): the extent of the data from smallest to largest value
Shape: overall appearance of distribution
Unusual features: gaps/clusters and outliers

12. Histogram C example roughly symmetrical with gaps at 30 and 40

13. Histogram C example uniform with possible outlier at 5

14. Displaying Distributions with Graphs
categorical versus quantitative
categorical: bar graphs, pie charts
quantitative: dotplots, histograms, stemplots, boxplots

15. Frequency Distributions
A frequency distribution is a table that displays the categories, frequencies, relative frequencies and/or cumulative relative frequencies.
The frequency for a particular category is the number of observed responses that fall into that category.
The corresponding relative frequency is the fraction or proportion of observed responses in the category.
The cumulative relative frequency is the fraction or proportion of observed responses in all categories so far including the current.

16. Creating Histograms
The difficulty with continuous data is that there are no natural categories. We must define our categories, or class intervals. The quantity often gives a rough estimate for an appropriate number of intervals. Or using Sturgis's Rule is to take classes, rounded to the nearest integer.

17. Example Exit Name Miles 1 Ohio Gateway * 16 Carlisle 25 1A New Castle8 17
Gettysburg Pike
9.8 2
Beaver Valley
3.4 18
Harrisburg West Shore
5.9 3
Cranberry
15.6 19
Harrisburg East
5.4 4
Butler Valley
10.7 20
Lebanon-Lancaster 5
Allegheny Valley
8.6 21
Reading
19.1 6
Pittsburgh
8.9 22
Morgantown
12.8 7
Irwin
10.8 12
Downingtown
13.7
New Stanton
8.1 24
Valley Forge
14.3 9
Donegal
15.2
Norristown
6.8 10
Somerset
19.2 26
Fort Washington 11
Bedford
35.6 27
Willow Grove
4.4
Breezewood
15.9 28
Philadelphia
8.4 13
Fort Littleton
18.1 29
Delaware Valley
6.4 14
Willow Hill
9.1 30 15
Blue Mountain
12.7

18. Stemplots Median: 62 6 7 5 4 3 2 8 9 1 Spread: from 22 to 91 4 8 5
8 5 2 6 1 2 5 8 3 5
Fairly symmetrical 2 5
No unusual
features 7 5 5
Key: 2|2 means 22 wpm

19. Alfred Hitchcock Stemplot13 12 11 10 9 8 1 9 5
Key: 8|1 means 81 minutes

20. Split Stemplot Similar to a histogram, we want to avoid too many
data points in a small range
ages of which a sample of 35 American mothers first gave birth 4 3 2 1
Key: 1|4 means 14 years old

21. Split Stemplot Split stemplot typically breaks each stem into
High (5-9) and Low(0-4) 3 1 4 2
Key: 1|4 means 14 years old

22. Split Stemplot Split stemplot typically breaks each stem into
High (5-9) and Low(0-4) 3H 2H 1H 4L 3L 2L 1L 4 3 2 1
Key: 1|4 means 14 years old

23. Split Stemplot Split stemplot typically breaks each stem into
High (5-9) and Low(0-4) 3H 2H 1H 4L 3L 2L 1L 4 3 2 1
Key: 1|4 means 14 years old

24. Split Stemplot Split stemplot typically breaks each stem into
High (5-9) and Low(0-4) 3H 2H 1H 4L 3L 2L 1L 4
Key: 1|4 means 14 years old

25. Back to Back Stemplots
9 3 8 4 1 6 5 4 3 2 1 4
5 4
5 2
Babe Ruth
Roger Maris 4 9 6 3 6 3
Key: 4 | 1 means 41

26. Babe Ruth vs. Roger Maris
Generally, we can see that Babe Ruth hit more home runs than Roger Maris.
The center of Babe Ruth is higher at 46 than Roger Maris at 24.5 home runs.
Roger Maris has an outlier at 61 while Ruth has no outliers.
Ruth has a higher spread from 22 to 60 than Maris from 8 to 39 if we exclude the outlier.
Both distributions are fairly symmetrical.